Frank solutions for Mathematics [English] Class 9 ICSE chapter 28 - Coordinate Geometry [Latest edition]

Find the value of 'a' and 'b' if
a. (a + 2,5 + b) = (1, 6)
b. (2a + b, a - 2b) = (7, 6)

State the quadrant in which each of the following point lies: A(-4, 3), B(2, -5), C(-5, -3), M(4, 8), P(-1, 9) and Z(4, -5)

State the axis on which the following points lie: J(0, -7), M(5, 0), P(-4, 0), R(0, 6) and W(2, 0)

Find the co-ordinates of points whose: Abscissa is 6 and ordinate is 2

Find the co-ordinates of points whose: Abscissa is 0 and ordinate is -3

Find the co-ordinates of points whose: Abscissa is 5 and ordinate is -1

Find the co-ordinates of points whose: Abscissa is -2 and ordinate is 0

Find the co-ordinates of points whose: Abscissa is -4 and ordinate is -7

Find the co-ordinates of points whose: Abscissa is 0 and ordinate is 0

Find the co-ordinates of points whose: Abscissa is -7 and ordinate is 4

Plot the following points on the graph paper: P(2, 5), Q(4, 0), R(0, 7), S(-3, 5), T(4, -4), U(0, -2) and V(-1, -4)

Plot the points O (0, 0), P (6, 0) and R (0, 5) on a graph. Find the coordinates of the point Q such that OPQR is a rectangle.

Plot the points A (3, 4) and C (-3, -2) on a graph. Find the coordinates of the point B and D such ABCD is a square. Also find the area of the square.

Plot the points (-2, 3), (3, 3), (5, -2) and (-5, -2) on a graph and join them in order. Name the figure you get.

Find if the following points are collinear or not by using a graph:
(i) (-2, -1), (0, 3) and (1, 5)
(ii) (1, 3), (-2, -4) and (3, 5)
(iii) (2, -1), (2, 5) and (2, 7)
(iv) (4, -1), (-5, -1) and (3, -1)

In each of the following, find the coordinates of the point whose abscissa is the solution of the first equation and ordinate is the solution of the second equation.

5 + 2x = ${\displaystyle 9:3\frac{1}{2}y+1}$ = 12 - 3y

In each of the following, find the coordinates of the point whose abscissa is the solution of the first equation and ordinate is the solution of the second equation.

(7 - x) + 7x = ${\displaystyle (x+5);\frac{2+3y}{2}}$ = 2y - 6

A rectangle PQRS is drawn on the coordinate axes such that P is the origin, PQ = 6 units and PS = 5 units. Find the coordinates of the vertices P, Q R and S. Also, find the area of the rectangle.

Express the equation 3x + 5y + 15 = 0 in the form such that:
a. x is subject to the formula
b. y is dependent variable and x is independent variable.

Draw a graph of each of the following equations: x + 5 = 0

Draw a graph of each of the following equations: y - 4 = 0

Draw a graph of each of the following equations: 2x = 7

Draw a graph of each of the following equations: 2y - 5 = 0

Draw a graph of each of the following equations: x = 0

Draw a graph of each of the following equations: y = 3

Draw a graph of each of the following equations: x + 6y = 15

Draw a graph of each of the following equations: 3x - 2y = 6

Draw a graph of each of the following equations: 3y + 2x = 11

Draw a graph of each of the following equations: 5x + 2y = 16

Draw a graph of each of the following equations: x + y - 3 = 0

Draw a graph of each of the following equations: x = -3y

Draw a graph of each of the following equations: y = ${\displaystyle \frac{5}{2}\times +\frac{2}{5}}$

Draw a graph of each of the following equations: ${\displaystyle \frac{x-2}{3}-\frac{y+1}{2}}$ = 0

Draw a graph of each of the following equations: 2(x - 5) = ${\displaystyle \frac{3}{4}(y-1)}$

Draw a graph of each of the following equations: y = ${\displaystyle \frac{3}{5}x-1}$

Draw a graph of the equation 3x - y = 7. From the graph find the value of:
(i) y, when x = 1
(ii) x, when y = 8

Draw a graph of the equation 2x - 3y = 15. From the graph find the value of:
(i) x, when y = 3
(ii) y, when x = 0

Draw a graph for each of the following equations and find the coordinates of the points where the line drawn meets the x-axis and y-axis: 2x + 3y = 12

Draw a graph for each of the following equations and find the coordinates of the points where the line drawn meets the x-axis and y-axis: ${\displaystyle \frac{2x}{5}+\frac{y}{2}}$ = 1

Draw a graph of the equation 2x + 3y + 5 = 0, from the graph find the value of:
(i) x, when y = -3
(ii) y, when x = 8

Draw a graph of the equation 5x - 3y = 1. From the graph find the value of:
(i) x, when y = 8
(ii) y, when x = 2

Draw the graph of the lines y = x + 2, y = 2x - 1 and y = 2 from x = -3 to 4, on the same graph paper. Check whether the lines drawn are parallel to each other.

Find the inclination and slope of a line which is equidistant from the x-axis.

Find the inclination and slope of a line which is equidistant from the y-axis.

Find the inclination and slope of a line which is intersecting x-axis at right angle.

Find the inclination and slope of a line which is perpendicular to y-axis.

Find the slope of the line whose inclination is given as 0°

Find the slope of the line whose inclination is given as 30°

Find the slope of the line whose inclination is given as 45°

Find the slope of the line whose inclination is given as 60°

Find the inclination of the line whose slope is 1

Find the inclination of the line whose slope is ${\displaystyle \sqrt{3}}$

Find the slope and y-intercept for each of the following equations: 3x - 8y + 24 = 0

Find the slope and y-intercept for each of the following equations: 6x = 7y - 12

Find the equation of the line, whose slope is 3 and y-intercept is 5.

Find the equation of the line, whose slope is 0 and y-intercept is -1.

Find the equation of the line, whose slope is 1 and y-intercept is 0.

Draw the graph of a line 2x + 3y = 6. From the graph, find the slope and y-intercept of the line.

Draw the graph of the lines represented by the equations x + y = 4 and 2x - y = 2 on the same graph. Find the coordinates of the point where they intersect

Draw the graph of the lines represented by the equations 3x - 2y = 4 and x + y = 3 on the same graph. Find the coordinates of the point where they intersect. State, whether the lines are perpendicular to each other.

Draw the graph of the lines represented by the equations 2x - y = 8 and 4x + 3y = 6 on the same graph. Find the co-ordinates of the point where they intersect.

Draw the graph of the lines represented by the equations 5y = 3x + 1 and y = 2x + 3 on the same graph. Find the coordinates of the point where they intersect.