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**Exercise 10.1 : ** Solutions of Questions on Page Number : **211**

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**Exercise 10.2 : ** Solutions of Questions on Page Number : **219**

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**Exercise 10.3 : ** Solutions of Questions on Page Number : **227**

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**Exercise Miscellaneous : ** Solutions of Questions on Page Number : **233**

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**Exercise Miscellaneousmiscellaneous : ** Solutions of Questions on Page Number : **234**

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Next Chapter 11 : Conic Sections >>
**Popular Articles**

Q1 :
**
**

Draw a quadrilateral in the Cartesian plane, whose vertices are (-4, 5), (0, 7), (5, -5) and (-4, -2). Also, find its area.

**Answer :**

Let ABCD be the given quadrilateral with vertices A (â€“4, 5), B (0, 7), C (5, â€“5), and D (â€“4, â€“2).

Then, by plotting A, B, C, and D on the Cartesian plane and joining AB, BC, CD, and DA, the given quadrilateral can be drawn as

To find the area of quadrilateral ABCD, we draw one diagonal, say AC.

Accordingly, area (ABCD) = area (ΔABC) + area (ΔACD)

We know that the area of a triangle whose vertices are
(*x*_{1},
*y*_{1}),
(*x*_{2},
*y*_{2}), and
(*x*_{3},
*y*_{3}) is

Therefore, area of ΔABC

Area of ΔACD

Thus, area (ABCD)

Answer needs Correction? Click Here

Q2 :
**
**

The base of an equilateral triangle with side 2*a* lies
along they *y*-axis such that the mid point of the base is
at the origin. Find vertices of the triangle.

**Answer :**

Let ABC be the given equilateral triangle with side 2*a*.

Accordingly, AB = BC = CA = 2*a*

Assume that base BC lies along the *y*-axis such that the
mid-point of BC is at the origin.

i.e., BO = OC = *a*, where O is the origin.

Now, it is clear that the coordinates of point C are (0,
*a*), while the coordinates of point B are (0,
â€“*a*).

It is known that the line joining a vertex of an equilateral triangle with the mid-point of its opposite side is perpendicular.

Hence, vertex A lies on the *y*-axis.

On applying Pythagoras theorem to ΔAOC, we obtain

(AC)^{2} = (OA)^{2} + (OC)^{2}

⇒
(2*a*)^{2} = (OA)^{2} +
*a*^{2}

⇒
4*a*^{2} â€“
*a*^{2} = (OA)^{2}

⇒
(OA)^{2} = 3*a*^{2}

⇒ OA =

∴Coordinates of point A =

Thus, the vertices of the given equilateral triangle are (0,
*a*), (0, â€“*a*), and or (0,
*a*), (0, â€“*a*), and.

Answer needs Correction? Click Here

Q3 :
**
**

Find the distance between and when: (i) PQ is parallel
to the *y*-axis, (ii) PQ is parallel to the *x*-axis.

**Answer :**

Q4 :
**
**

Find a point on the *x*-axis, which is equidistant from the
points (7, 6) and (3, 4).

**Answer :**

Q5 :
**
**

Find the slope of a line, which passes through the origin, and the mid-point of

the line segment joining the points P (0, -4) and B (8, 0).

**Answer :**

Q6 :
**
**

Without using the Pythagoras theorem, show that the points (4, 4), (3, 5) and (-1, -1) are the vertices of a right angled triangle.

**Answer :**

Q7 :
**
**

Find the slope of the line, which makes an angle of
30° with the positive direction of
*y*-axis measured anticlockwise.

**Answer :**

Q8 :
**
**

Find the value of *x* for which the points (*x*,
-1), (2, 1) and (4, 5) are collinear.

**Answer :**

Q9 :
**
**

Without using distance formula, show that points (-2, -1), (4, 0), (3, 3) and

(-3, 2) are vertices of a parallelogram.

**Answer :**

Q10 :
**
**

Find the angle between the *x*-axis and the line joining the
points (3, -1) and (4,
-2).

**Answer :**

Q11 :
**
**

The slope of a line is double of the slope of another line. If tangent of the angle between them is, find the slopes of he lines.

**Answer :**

Q12 :
**
**

A line passes through. If slope of the line
is *m*, show that.

**Answer :**

Q13 :
**
**

If three point (*h,* 0), (*a, b*) and (0*, k*) lie
on a line, show that.

**Answer :**

Q14 :
**
**

Consider the given population and year graph. Find the slope of the line AB and using it, find what will be the population in the year 2010?

**Answer :**

Q1 :
**
**

Write the equations for the *x* and *y*-axes.

**Answer :**

Q2 :
**
**

Find the equation of the line which passes through the point (â€“4, 3) with slope.

**Answer :**

Q3 :
**
**

Find the equation of the line which passes though (0, 0) with
slope *m*.

**Answer :**

Q4 :
**
**

Find the equation of the line which passes though and is
inclined with the *x*-axis at an angle of
75°.

**Answer :**

Q5 :
**
**

Find the equation of the line which intersects the *x*-axis
at a distance of 3 units to the left of origin with slope
-2.

**Answer :**

Q6 :
**
**

Find the equation of the line which intersects the *y*-axis
at a distance of 2 units above the origin and makes an angle of
30° with the positive direction of the
*x*-axis.

**Answer :**

Q7 :
**
**

Find the equation of the line which passes through the points (-1, 1) and (2, -4).

**Answer :**

Q8 :
**
**

Find the equation of the line which is at a perpendicular
distance of 5 units from the origin and the angle made by the
perpendicular with the positive *x*-axis is
30°

**Answer :**

Q9 :
**
**

The vertices of ΔPQR are P (2, 1), Q (-2, 3) and R (4, 5). Find equation of the median through the vertex R.

**Answer :**

Q10 :
**
**

Find the equation of the line passing through (-3, 5) and perpendicular to the line through the points (2, 5) and (-3, 6).

**Answer :**

Q11 :
**
**

A line perpendicular to the line segment joining the points (1,
0) and (2, 3) divides it in the ratio 1:*n*. Find the
equation of the line.

**Answer :**

Q12 :
**
**

Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point (2, 3).

**Answer :**

Q13 :
**
**

Find equation of the line passing through the point (2, 2) and cutting off intercepts on the axes whose sum is 9.

**Answer :**

Q14 :
**
**

Find equation of the line through the point (0, 2) making an
angle with
the positive *x*-axis. Also, find the equation of line
parallel to it and crossing the *y*-axis at a distance of 2
units below the origin.

**Answer :**

Q15 :
**
**

The perpendicular from the origin to a line meets it at the point (- 2, 9), find the equation of the line.

**Answer :**

Q16 :
**
**

The length L (in centimetre) of a copper rod is a linear function of its Celsius temperature C. In an experiment, if L = 124.942 when C = 20 and L = 125.134 when C = 110, express L in terms of C.

**Answer :**

Q17 :
**
**

The owner of a milk store finds that, he can sell 980 litres of milk each week at Rs 14/litre and 1220 litres of milk each week at Rs 16/litre. Assuming a linear relationship between selling price and demand, how many litres could he sell weekly at Rs 17/litre?

**Answer :**

Q18 :
**
**

P (*a, b*) is the mid-point of a line segment between axes.
Show that equation of the line is

**Answer :**

Q19 :
**
**

Point R (*h, k*) divides a line segment between the axes in
the ratio 1:2. Find equation of the line.

**Answer :**

Q20 :
**
**

By using the concept of equation of a line, prove that the three points (3, 0),

(-2, -2) and (8, 2) are collinear.

**Answer :**

Q1 :
**
**

Reduce the following equations into slope-intercept form and find
their slopes and the *y*-intercepts.

(i) *x* + 7*y* = 0 (ii) 6*x* + 3*y*
- 5 = 0 (iii) *y* = 0

**Answer :**

Q2 :
**
**

Reduce the following equations into intercept form and find their intercepts on the axes.

(i) 3*x* + 2*y* - 12 = 0 (ii)
4*x* - 3*y* = 6 (iii) 3*y* + 2
= 0.

**Answer :**

Q3 :
**
**

Reduce the following equations into normal form. Find their
perpendicular distances from the origin and angle between
perpendicular and the positive
*x*-axis.

(i) (ii)
*y* â€“ 2 = 0
(iii) *x*
â€“ *y* =
4

**Answer :**

Q4 :
**
**

Find the distance of the point (-1, 1) from
the line 12(*x* + 6) = 5(*y* - 2).

**Answer :**

Q5 :
**
**

Find the points on the *x*-axis, whose distances from the
line are 4 units.

**Answer :**

Q6 :
**
**

Find the distance between parallel lines

(i) 15*x* + 8*y* - 34 = 0 and
15*x* + 8*y* + 31 = 0

(ii) *l* (*x* + *y*) + *p* = 0 and *l*
(*x* + *y*) - *r* = 0

**Answer :**

Q7 :
**
**

Find equation of the line parallel to the line 3*x*
- 4*y* + 2 = 0 and passing through the
point (-2, 3).

**Answer :**

Q8 :
**
**

Find equation of the line perpendicular to the line *x*
- 7*y* + 5 = 0 and having *x*
intercept 3.

**Answer :**

Q9 :
**
**

Find angles between the lines

**Answer :**

Q10 :
**
**

The line through the points (*h*, 3) and (4, 1) intersects
the line 7*x* - 9*y*
- 19 = 0*.* at right angle. Find the
value of *h*.

**Answer :**

Q11 :
**
**

Prove that the line through the point (*x*_{1},
*y*_{1}) and parallel to the line A*x +* B*y
+* C = 0 is A (*x -x*_{1})
*+* B (*y - y*_{1}) = 0.

**Answer :**

Q12 :
**
**

Two lines passing through the point (2, 3) intersects each other at an angle of 60°. If slope of one line is 2, find equation of the other line.

**Answer :**

Q13 :
**
**

Find the equation of the right bisector of the line segment
joining the points (3, 4) and (*-*1, 2).

**Answer :**

Q14 :
**
**

Find the coordinates of the foot of perpendicular from the point
(*-*1, 3) to the line 3*x*
- 4*y* - 16 = 0.

**Answer :**

Q15 :
**
**

The perpendicular from the origin to the line *y = mx + c*
meets it at the point

(*-*1, 2). Find the values of *m*
and *c*.

**Answer :**

Q16 :
**
**

If *p* and *q* are the lengths of perpendiculars from
the origin to the lines *x* cos
*ÃŽÂ¸* -
*y* sin *ÃŽÂ¸* = *k* cos
2*ÃŽÂ¸* and *x* sec
*ÃŽÂ¸*+ *y* cosec
*ÃŽÂ¸* = *k*, respectively,
prove that *p*^{2} + 4*q*^{2} =
*k*^{2}

**Answer :**

Q17 :
**
**

In the triangle ABC with vertices A (2, 3), B (4,
*-*1) and C (1, 2), find the equation
and length of altitude from the vertex A.

**Answer :**

Q18 :
**
**

If *p* is the length of perpendicular from the origin to the
line whose intercepts on the axes are *a* and *b*, then
show that.

**Answer :**

Q1 :
**
**

Find the values of *k* for which the lineis

(a) Parallel to the *x*-axis,

(b) Parallel to the *y*-axis,

(c) Passing through the origin.

**Answer :**

Q2 :
**
**

Find the values of *θ*and *p*,
if the equation is the normal form
of the line.

**Answer :**

Q3 :
**
**

Find the equations of the lines, which cut-off intercepts on the axes whose sum and product are 1 and -6, respectively.

**Answer :**

Q4 :
**
**

What are the points on the *y*-axis whose distance from the
line is 4 units.

**Answer :**

Q5 :
**
**

Find the perpendicular distance from the origin to the line joining the points

**Answer :**

Q6 :
**
**

Find the equation of the line parallel to *y*-axis and drawn
through the point of intersection of the lines *x*
- 7*y* + 5 = 0 and 3*x* + *y*
= 0.

**Answer :**

Q7 :
**
**

Find the equation of a line drawn perpendicular to the line
through the point, where
it meets the *y*-axis.

**Answer :**

Q8 :
**
**

Find the area of the triangle formed by the lines *y*
-*x* = 0, *x* + *y* = 0 and
*x* - *k* = 0.

**Answer :**

Q9 :
**
**

Find the value of *p* so that the three lines 3*x* +
*y* - 2 = 0, *px* + 2*y*
- 3 = 0 and 2*x* -
*y* - 3 = 0 may intersect at one point.

**Answer :**

Q10 :
**
**

If three lines whose equations are

concurrent, then show that

**Answer :**

Q11 :
**
**

Find the equation of the lines through the point (3, 2) which
make an angle of 45° with the line
*x* -2*y* = 3.

**Answer :**

Q12 :
**
**

Find the equation of the line passing through the point of
intersection of the lines 4*x* + 7*y*
- 3 = 0 and 2*x* -
3*y* + 1 = 0 that has equal intercepts on the axes.

**Answer :**

Q1 :
**
**

Show that the equation of the line passing through the
origin and making an angle
*θ*with the
line.

**Answer :**

Q2 :
**
**

In what ratio, the line joining (-1, 1) and (5, 7) is divided by the line

*x* + *y* = 4?

**Answer :**

Q3 :
**
**

Find the distance of the line 4*x* + 7*y* + 5 = 0 from
the point (1, 2) along the line 2*x* -
*y* = 0.

**Answer :**

Q4 :
**
**

Find the direction in which a straight line must be drawn through
the point (-1, 2) so that its point of
intersection with the line *x* + *y* = 4 may be at a
distance of 3 units from this point.

**Answer :**

Q5 :
**
The hypotenuse of a right angled triangle has its ends at the
points (1, 3) and
(-4, 1). Find the
equation of the legs (perpendicular sides) of the triangle. **

**Answer :**

Q6 :
**
**

Find the image of the point (3, 8) with respect to the line
*x* + 3*y* = 7 assuming the line to be a plane mirror.

**Answer :**

Q7 :
**
**

If the lines *y* = 3*x* + 1 and 2*y* = *x* +
3 are equally inclined to the line *y* = *mx* + 4, find
the value of *m*.

**Answer :**

Q8 :
**
**

If sum of the perpendicular distances of a variable point P
(*x*, *y*) from the lines *x* + *y*
- 5 = 0 and 3*x* -
2*y* + 7 = 0 is always 10. Show that P must move on a line.

**Answer :**

Q9 :
**
**

Find equation of the line which is equidistant from parallel
lines 9*x* + 6*y* - 7 = 0 and
3*x* + 2*y* + 6 = 0.

**Answer :**

Q10 :
**
**

A ray of light passing through the point (1, 2) reflects on the
*x*-axis at point A and the reflected ray passes through the
point (5, 3). Find the coordinates of A.

**Answer :**

Q11 :
**
**

Prove that the product of the lengths of the perpendiculars drawn from the points

**Answer :**

Q12 :
**
**

A person standing at the junction (crossing) of two straight
paths represented by the equations 2*x*
- 3*y* + 4 = 0 and 3*x* + 4*y*
- 5 = 0 wants to reach the path whose
equation is 6*x* - 7*y* + 8 = 0 in
the least time. Find equation of the path that he should follow.

**Answer :**

Maths - Maths : CBSE ** NCERT ** Exercise Solutions for Class 11th for ** Straight Lines ** ( Exercise 10.1, 10.2, 10.3, miscellaneous, miscellaneousmiscellaneous ) will be available online in PDF book form soon. The solutions are absolutely Free. Soon you will be able to download the solutions.

- Maths : Chapter 3 - Trigonometric Functions Class 11
- Maths : Chapter 4 - Principle of Mathematical Induction Class 11
- Maths : Chapter 5 - Complex Numbers and Quadratic Equations Class 11
- Maths : Chapter 2 - Relations and Functions Class 11
- Maths : Chapter 1 - Sets Class 11
- Maths : Chapter 9 - Sequences and Series Class 11
- Maths : Chapter 6 - Linear Inequalities Class 11
- Maths : Chapter 7 - Permutations and Combinations Class 11
- Maths : Chapter 13 - Limits and Derivatives Class 11
- Maths : Chapter 8 - Binomial Theorem Class 11

Exercise 10.1 |

Question 1 |

Question 2 |

Question 3 |

Question 4 |

Question 5 |

Question 6 |

Question 7 |

Question 8 |

Question 9 |

Question 10 |

Question 11 |

Question 12 |

Question 13 |

Question 14 |

Exercise Miscellaneous |

Question 1 |

Question 2 |

Question 3 |

Question 4 |

Question 5 |

Question 6 |

Question 7 |

Question 8 |

Question 9 |

Question 10 |

Question 11 |

Question 12 |

Exercise Miscellaneousmiscellaneous |

Question 1 |

Question 2 |

Question 3 |

Question 4 |

Question 5 |

Question 6 |

Question 7 |

Question 8 |

Question 9 |

Question 10 |

Question 11 |

Question 12 |