## ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 12 Equation of a Straight Line Ex 12.1

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 12 Equation of a Straight Line Ex 12.1

Question 1.

Find the slope of a line whose inclination is

(i) 45°

(ii) 30°

Solution:

Question 2.

Find the inclination of a line whose gradient is

(i) 1

(ii) √3

(iii) \(\frac { 1 }{ \sqrt { 3 } } \)

Solution:

Question 3.

Find the equation of a straight line parallel 1 to x-axis which is at a distance

(i) 2 units above it

(ii) 3 units below it.

Solution:

Question 4.

Find the equation of a straight line parallel to y-axis which is at a distance of:

(i) 3 units to the right

(ii) 2 units to the left.

Solution:

Question 5.

Find the equation of a straight line parallel to the y-axis and passing through the point (-3, 5).

Solution:

Question 6.

Find the equation of the a line whose

(i) slope = 3, y-intercept = -5

(ii) slope = \(– \frac { 2 }{ 7 } \), y-intercept = 3

(iii) gradient = √3, y-intercept = \(– \frac { 4 }{ 3 } \)

(iv) inclination = 30°, y-intercept = 2

Solution:

Question 7.

Find the slope and y-intercept of the following lines:

(i) x – 2y – 1 = 0

(ii) 4x – 5y – 9 = – 0

(iii) 3x +5y + 7 = 0

(iv) \(\frac { x }{ 3 } +\frac { y }{ 4 } =1\)

(v) y – 3 = 0

(vi) x – 3 = 0

Solution:

Question 8.

The equation of the line PQ is 3y – 3x + 7 = 0

(i) Write down the slope of the line PQ.

(ii) Calculate the angle that the line PQ makes with the positive direction of the x-axis.

Solution:

Question 9.

The given figure represents the line y = x + 1 and y = √3x – 1. Write down the angles which the lines make with the positive direction of the x-axis. Hence determine θ.

Solution:

Question 10.

Find the value of p, given that the line \(\frac { y }{ 2 } =x-p\) passes through the point (-4, 4) (1992).

Solution:

Question 11.

Given that (a, 2a) lies on the line \(\frac { y }{ 2 } =3x-6\) find the value of a.

Solution:

Question 12.

The graph of the equation y = mx + c passes through the points (1, 4) and (-2, -5). Determine the values of m and c.

Solution:

Question 13.

Find the equation of the line passing through the point (2, -5) and making an intercept of -3 on the y-axis.

Solution:

Question 14.

Find the equation of a straight line passing through (-1, 2) and whose slope is \(\\ \frac { 2 }{ 5 } \).

Solution:

Question 15.

Find the equation of a straight line whose inclination is 60° and which passes through the point (0, -3).

Solution:

Question 16.

Find the gradient of a line passing through the following pairs of points.

(i) (0, -2), (3, 4)

(ii) (3, -7), (-1, 8)

Solution:

Question 17.

The coordinates of two points E and F are (0, 4) and (3, 7) respectively. Find:

(i) The gradient of EF

(ii) The equation of EF

(iii) The coordinates of the point where the line EF intersects the x-axis.

Solution:

Question 18.

Find the intercepts made by the line 2x – 3y + 12 = 0 on the co-ordinate axis.

Solution:

Question 19.

Find the equation of the line passing through the points P (5, 1) and Q (1, -1). Hence, show that the points P, Q and R (11, 4) are collinear.

Solution:

Question 20.

Find the value of ‘a’ for which the following points A (a, 3), B (2, 1) and C (5, a) are collinear. Hence find the equation of the line.

Solution:

Question 21.

Use a graph paper for this question. The graph of a linear equation in x and y, passes through A (-1, -1) and B (2, 5). From your graph, find the values of h and k, if the line passes through (h, 4) and (½, k). (2005)

Solution:

Question 22.

ABCD is a parallelogram where A (x, y), B (5, 8), C (4, 7) and D (2, -4). Find

(i) the coordinates of A

(ii) the equation of the diagonal BD.

Solution:

Question 23.

In ∆ABC, A (3, 5), B (7, 8) and C (1, -10). Find the equation of the median through A.

Solution:

Question 24.

Find the equation of a line passing through the point (-2, 3) and having x-intercept 4 units. (2002)

Solution:

Question 25.

Find the equation of the line whose x-intercept is 6 and y-intercept is -4.

Solution:

Question 26.

Write down the equation of the line whose gradient is \(\\ \frac { 1 }{ 2 } \) and which passes through P where P divides the line segment joining A (-2, 6) and B (3, -4) in the ratio 2 : 3. (2001)

Solution:

Question 27.

Find the equation of the line passing through the point (1, 4) and intersecting the line x – 2y – 11 = 0 on the y-axis.

Solution:

Question 28.

Find the equation of the straight line containing the point (3, 2) and making positive equal intercepts on axes.

Solution:

Question 29.

Three vertices of a parallelogram ABCD taken in order are A (3, 6), B (5, 10) and C (3, 2) find:

(i) the coordinates of the fourth vertex D.

(ii) length of diagonal BD.

(iii) equation of side AB of the parallelogram ABCD. (2015)

Solution:

Question 30.

A and B are two points on the x-axis and y-axis respectively. P (2, -3) is the midpoint of AB. Find the

(i) the co-ordinates of A and B.

(ii) the slope of the line AB.

(iii) the equation of the line AB. (2010)

Solution:

Question 31.

Find the equations of the diagonals of a rectangle whose sides are x = -1, x = 2 , y = -2 and y = 6.

Solution:

Question 32.

Find the equation of a straight line passing through the origin and through the point of intersection of the lines 5x + 1y – 3 and 2x – 3y = 7

Solution:

Question 33.

Point A (3, -2) on reflection in the x-axis is mapped as A’ and point B on reflection in the y-axis is mapped onto B’ (-4, 3).

(i) Write down the co-ordinates of A’ and B.

(ii) Find the slope of the line A’B, hence find its inclination.

Solution: