M l aggarwal understanding icse mathematics class 10 Solutions for Chapter 11 equation of straight line

Exercises in Chapter 11 equation of straight line Grade 10

Equation of Straight Line Exercise 12.1

Equation of Straight Line Exercise 12.2

Questions in Equation of Straight Line Exercise 12.1

Find the slope of a line whose inclination is 45°

Find the slope of a line whose inclination is 30°

Find the inclination of a line whose gradient is 1

Find the inclination of a line whose gradient is √3

Find the equation of a straight line parallel to x-axis which is at a distance 2 units above it.

Find the equation of a line whose gradient = √3, y-intercept = -4/3

Find the equation of a line whose inclination = 30°, y-intercept = 2

Find the slope and y-intercept of the following lines: x – 2y – 1 = 0

Find the slope and y-intercept of the following lines: 4x – 5y – 9 = 0

Find the slope and y-intercept of the following lines: 3x + 5y + 7 = 0

Find the slope and y-intercept of the following lines: x/3 + y/4 = 1

Find the slope and y-intercept of the following lines: y – 3 = 0

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

Find the equation of a straight line parallel to x-axis which is at a distance 3 units below it.

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

Find the equation of a straight line parallel to y-axis which is at a distance of: 2 units to the left.

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.

Find the equation of a line whose slope = 3, y-intercept = – 5

Find the equation of a line whose slope = -2/7, y-intercept = 3

Find the equation of a straight line parallel to y-axis which is at a distance of: 3 units to the right

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

Write down the slope of the line PQ.

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

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

Find the value of p, given that the line y/2 = x – p passes through the point (– 4, 4)

Given that (a, 2a) lies on the line y/2 = 3x – 6. Find the value of a.

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

Find the equation of a straight line passing through (– 1, 2) and whose slope is 2/5.

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

Find the slope and y-intercept of the following lines: x – 3 = 0

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

Find the equation of the diagonal BD.

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

(3, – 7), (– 1, 8)

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

Find: The gradient of EF

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

Find: The equation of EF

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

Find: The coordinates of the point where the line EF intersects the x-axis.

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

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.

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).

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

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

Find the coordinates of A.

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

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

Write down the equation of the line whose gradient is 3/2 and which passes through P where P divides the line segment joining A (– 2, 6) and B (3, – 4) in the ratio 2 : 3.

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

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

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

Find the equation of the line AB.

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

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).

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

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).

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

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

Find the the co-ordinates of A and B.

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

find: the coordinates of the fourth vertex D.

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

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.

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

find: equation of side AB of the parallelogram ABCD.

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

Find the inclination of a line whose gradient is 1/√3

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

(0, – 2), (3, 4)

Questions in Equation of Straight Line Exercise 12.2

Lines 2x – by + 5 = 0 and ax + 3y = 2 are parallel. Find the relation connecting a and b.

State which one of the following is true: The straight lines y = 3x – 5 and 2y = 4x + 7 are

(i) parallel

(ii) perpendicular

(iii) neither parallel nor perpendicular.

If 6x + 5y – 7 = 0 and 2px + 5y + 1 = 0 are parallel lines, find the value of p.

Find the equation of the line passing through (0, 4) and parallel to the line 3x + 5y + 15 = 0.

Given that the line y/2 = x – p and the line ax + 5 = 3y are parallel, find the value of a.

If the lines y = 3x + 7 and 2y + px = 3 perpendicular to each other, find the value of p.

If the straight lines kx – 5y + 4 = 0 and 4x – 2y + 5 = 0 are perpendicular to each other. Find the value of k.

If the lines 3x + by + 5 = 0 and ax – 5y + 7 = 0 are perpendicular to each other, find the relation connecting a and b.

Is the line through (– 2, 3) and (4, 1) perpendicular to the line 3x = y + 1? Does the line 3x = y + 1 bisect the join of (– 2, 3) and (4, 1).

The line through A (– 2, 3) and B (4, b) is perpendicular to the line 2x – 4y = 5.

Find the value of b.

If the lines 3x + y = 4, x – ay + 7 = 0 and bx + 2y + 5 = 0 form three consecutive sides of a rectangle, find the value of a and b.

Find the equation of a line, which has the y-intercept 4, and is parallel to the line 2x – 3y – 7 = 0.

Find the coordinates of the point where it cuts the x-axis.

Find the equation of a straight line perpendicular to the line 2x + 5y + 7 = 0 and with y-intercept – 3 units.

Find the equation of a st. line perpendicular to the line 3x – 4y + 12 = 0 and having same y-intercept as 2x – y + 5 = 0.

Find the equation of the line which is parallel to 3x – 2y = – 4 and passes through the point (0, 3).

Find the equation of a straight line passing through the intersection of 2x + 5y – 4 = 0 with x-axis and parallel to the line 3x – 7y + 8 = 0.

The equation of a line is y = 3x – 5. Write down the slope of this line and the intercept made by it on the y-axis. Hence or otherwise, write down the equation of a line which is parallel to the line and which passes through the point (0, 5).

Write down the equation of the line perpendicular to 3x + 8y = 12 and passing through the point (– 1, – 2).

The line 4x – 3y + 12 = 0 meets the x-axis at A. Write down the co-ordinates of A.

Determine the equation of the line passing through A and perpendicular to 4x – 3y + 12 = 0.

Find the equation of the line that is parallel to 2x + 5y – 7 = 0 and passes through the mid-point of the line segment joining the points (2, 7) and (– 4, 1).

Find the equation of the line that is perpendicular to 3x + 2y – 8 = 0 and passes through the mid-point of the line segment joining the points (5, – 2) and (2, 2).

Prove that the line through (0, 0) and (2, 3) is parallel to the line through (2, – 2) and (6, 4).

The equation of a line is 3x + 4y – 7 = 0.

Find the slope of the line.

The equation of a line is 3x + 4y – 7 = 0.

Find the equation of a line perpendicular to the given line and passing through the intersection of the lines x – y + 2 = 0 and 3x + y – 10 = 0.

Prove that the line through (– 2, 6) and (4, 8) is perpendicular to the line through (8, 12) and (4, 24).

Find the equation of the line perpendicular from the point (1, – 2) on the line 4x – 3y – 5 = 0. Also find the co-ordinates of the foot of perpendicular.

Show that the triangle formed by the points A (1, 3), B (3, – 1) and C (– 5, – 5) is a right-angled triangle by using slopes.

Find the equation of the line through the point (– 1, 3) and parallel to the line joining the points (0, – 2) and (4, 5).

Are the vertices of a triangle.

Find the coordinates of the centroid G of the triangle.

Are the vertices of a triangle.

Find the equation of the line through G and parallel to AC.

The line through P (5, 3) intersects y-axis at Q.

Write the slope of the line.

The line through P (5, 3) intersects y-axis at Q.

Write the equation of the line.

In the adjoining diagram, write down the co-ordinates of the points A, B and C.

In the adjoining diagram, write down the equation of the line through A parallel to BC.

Find the equation of the line through (0, – 3) and perpendicular to the line joining the points (– 3, 2) and (9, 1).

A (2, – 4), B (3, 3) and C (– 1, 5) are the vertices of triangle ABC.

Find the equation of: the median of the triangle through A.

The vertices of a triangle are A (10, 4), B (4, – 9) and C (– 2, – 1). Find the equation of the altitude through A. The perpendicular drawn from a vertex of a triangle to the opposite side is called altitude.

The line through P (5, 3) intersects y-axis at Q.

Find the coordinates of Q.