M l aggarwal understanding icse mathematics class 9 Solutions for Chapter 19 coordinate geometry

Find the coordinates of points whose

(i) abscissa is 3 and ordinate -4.

(ii)abscissa is -3/2 and ordinate 5.

\text { (iii)whose abscissa is }-1 \frac{2}{3} \text { and ordinate is }-2 \frac{1}{4}

(iv) whose ordinate is 5 and abscissa is -2

(v) whose abscissa is -2 and lies on the x-axis.

(vi) whose ordinate is 3/2 and lies on the y-axis.

In which quadrant or on which axis each of the following points lies?

(-3, 5), (4, -1) (2, 0), (2, 2), (-3, -6)

Which of the following points lie on

(i) x-axis? (ii) y-axis?

A (0, 2), B (5, 6), C (23, 0), D (0, 23), E (0, -4), F (-6, 0), G (√3,0)

Plot the following points on the same graph paper :

A (3, 4), B (-3, 1), C (1, -2), D (-2, -3), E (0, 5), F (5, 0), G (0, -3), H (-3, 0).

Write the co-ordinates of the points A, B, C, D, E, F, G and H shown in the adjacent figure.

coordinates,

In which quadrants are the points A, B, C and D of problem 3 located ?

Plot the following points on the same graph paper :

A(2, 5/2), B(-3/2, 3), C(1/2, -3/2) and D(-5/2, -1/2).

Plot the following points on the same graph paper.

A(4/3, -1), B(7/2, 5/3), C(13/6,0), D(-5/3,-5/2).

Plot the following points and check whether they are collinear or not:

(i) (1,3), (-1,-1) and (-2,-3)

(ii) (1,2), (2,-1) and (-1, 4)

(iii) (0,1), (2, -2) and (2/3,0).

Plot the point P(-3, 4). Draw PM and PN perpendiculars to the x-axis and y-axis respectively. State the coordinates of the points M and N.

Plot the points A (1,2), B (-4,2), C (-4, -1) and D (1, -1). What kind of quadrilateral is ABCD ? Also find

the area of the quadrilateral ABCD.

Plot the points (0,2), (3,0), (0, -2) and (-3,0) on a graph paper. Join these points (in order). Name the

figure so obtained and find the area of the figure obtained.

Three vertices of a square are A (2,3), B(-3, 3), and C (-3, -2). Plot these points on a graph paper and

hence use it to find the coordinates of the fourth vertex. Also, find the area of the square.

Write the co-ordinates of the vertices of a rectangle which is 6 units long and 4 units wide if the

rectangle is in the first quadrant, its longer side lies on the x-axis and one vertex is at the origin.

Repeat problem 12 assuming that the rectangle is in the third quadrant with all other conditions

remaining the same.

The adjoining figure shows an equilateral triangle OAB with each side = 2a units. Find the coordinates

of the vertices.

In the given figure, PQR is equilateral. If the coordinates of the points Q and R are (0, 2) and (0, -2)

respectively, find the coordinates of the point P.

Draw the graphs of the following linear equations :

(i) 2x +y+ 3 = 0

(ii) x- 5y- 4 = 0

Draw the graph of 3y = 12-2x. Take 2cm = 1 unit on both axes.

Draw the graph of 5x+6y-30 = 0 and use it to find the area of the triangle formed by the line and the co

ordinate axes.

Draw the graph of 4x-3y+12 = 0 and use it to find the area of the triangle formed by the line and the co

ordinate axes. Take 2 cm = 1 unit on both axes.

Draw the graph of the equation y = 3x – 4. Find graphically.

(i) the value of y when x = -1

(ii) the value of x when y = 5.

The graph of a linear equation in x and y passes through (4, 0) and (0, 3). Find the value of k if the graph

passes through (A, 1.5).

Use the table given alongside to draw the graph of a straight line. Find, graphically the values of a and b.

Solve the following equations graphically: 3x-2y = 4, 5x-2y = 0

. Solve the following pair of equations graphically. Plot at least 3 points for each straight line 2x -7y = 6, 5x

-8y = -4.

Using the same axes of co-ordinates and the same unit, solve graphically.

x+y = 0, 3x – 2y = 10

Take 1 cm to represent 1 unit on each axis to draw the graphs of the equations 4x- 5y = -4 and 3x = 2y – 3

on the same graph sheet (same axes). Use your graph to find the solution of the above simultaneous

equations.

Solve the following simultaneous equations graphically, x + 3y = 8, 3x = 2 + 2y

Solve graphically the simultaneous equations 3y = 5 – x, 2x = y + 3

(Take 2cm = 1 unit on both axes).

Use graph paper for this question.

Take 2 cm = 1 unit on both axes.

(i) Draw the graphs of x +y + 3 = 0 and 3x-2y + 4 = 0. Plot only three points per line.

(ii) Write down the co-ordinates of the point of intersection of the lines.

(iii) Measure and record the distance of the point of intersection of the lines from the origin in cm

Solve the following simultaneous equations, graphically :

2x-3y + 2 = 4x+ 1 = 3x – y + 2

Use graph paper for this question.

(i) Draw the graphs of 3x -y – 2 = 0 and 2x + y – 8 = 0. Take 1 cm = 1 unit on both axes and plot three points

per line.

(ii) Write down the co-ordinates of the point of intersection and the area of the triangle formed by the lines

and the x-axis

Solve the following system of linear equations graphically : 2x -y – 4 = 0, x + y + 1 = 0. Hence, find the

area of the triangle formed by these lines and the y-axis.

. Solve graphically the following equations: x + 2y = 4, 3x – 2y = 4

Take 2 cm = 1 unit on each axis. Write down the area of the triangle formed by the lines and the x-axis.

On graph paper, take 2 cm to represent one unit on both the axes, draw the lines : x + 3 = 0, y – 2 = 0,

2x + 3y = 12 .

Write down the co-ordinates of the vertices of the triangle formed by these lines.

. Find graphically the co-ordinates of the vertices of the triangle formed by the lines y = 0, y = x and 2x +

3y= 10. Hence find the area of the triangle formed by these lines.

A is a point on y-axis whose ordinate is 4 and B is a point on x-axis whose abscissa is -3. Find the length

of the line segment AB.

Find the value of a, if the distance between the points A (-3, -14) and B (a, -5) is 9 units.

Find the point on the x-axis which, is equidistant from the points (2, -5) and (-2, 9).

Find the value of x such that PQ = QR where the coordinates of P, Q and R are (6, -1), (1, 3) and (x, 8)

respectively.

If Q(0, 1) is equidistant from P (5, -3) and R (x, 6) find the values of x.

Using distance formula, show that (3, 3) is the centre of the circle passing through the points (6, 2), (0, 4)

and (4, 6).

Using distance formula, show that the points A (3, 1), B (6, 4) and C (8, 6) are collinear.

Check whether the points (5, -2), (6, 4) and (7, -2) are the vertices of an isosceles triangle.

Show that the points (1, 1), (- 1, – 1) and (-√3,√3) form an equilateral triangle.

Show that the points (7, 10), (-2, 5) and (3, -4) are the vertices of an isosceles right triangle.

The points A (0, 3), B (- 2, a) and C (- 1, 4) are the vertices of a right angled triangle at A, find the value

of a.

If P (2, -1), Q (3, 4), R (-2, 3) and S (-3, -2) be four points in a plane, show that PQRS is a rhombus but

not a square. Find the area of the rhombus.

Name the type of quadrilateral formed by the following points and give reasons for your answer :

(i) (-1, -2), (1, 0), (-1, 2), (-3, 0)

(ii) (4, 5), (7, 6), (4, 3), (1, 2)

If two opposite vertices of a square are (3, 4) and (1, -1), find the coordinates of the other two vertices.