Selina solutions for Concise Mathematics [English] Class 9 ICSE chapter 23 - Co-ordinate Geometry [Latest edition]

In equation 2x − 5 = 0; ordinate is ______.

In equation y = `3 + "4x"/5` the independent 5 variable is ______.

If (2x − 1, y + 5) = (3, 10), the values of x and y are ______.

(5, −7) belongs to ______.

Abscissa of a point is the solution of equation 3x − 2 = 7 and its ordinate is the solution of equation 8 − 3y = 2. The point is ______.

For the equation given below; name the dependent and independent variables.
y = `(4)/(3)x` - 7

For the equation given below; name the dependent and independent variables.
 x = 9y + 4

For the equation given below; name the dependent and independent variables.
x = `(5y + 3)/(2)`

For each equation given below; name the dependent and independent variables.
y = `(1)/(7)` (6x + 5)

Plot the following points on the same graph paper:
(i) (8, 7)
(ii) (3, 6)
(iii) (0, 4)
(iv) (0, -4)
(v) (3, -2)
(vi) (-2, 5)
(vii) (-3, 0)
(viii) (5, 0)
(ix) (-4, -3)

Find the values of x and y if:
(x - 1, y + 3) = (4, 4)

Find the values of x and y if:
(3x + 1, 2y - 7) = (9, - 9)

Find the values of x and y if:
(5x - 3y, y - 3x) = (4, -4)

Use the graph given alongside, to find the coordinates of the point (s) satisfying the given condition:
(i) The abscissa is 2.
(ii)The ordinate is 0.
(iii) The ordinate is 3.
(iv) The ordinate is -4.
(v) The abscissa is 5.
(vi) The abscissa is equal to the ordinate.
(vii) The ordinate is half of the abscissa.

State, true or false:
The ordinate of a point is its x-co-ordinate.

State, true or false:
The origin is in the first quadrant.

State, true or false:
The y-axis is the vertical number line.

State, true or false:
Every point is located in one of the four quadrants.

State, true or false:
If the ordinate of a point is equal to its abscissa; the point lies either in the first quadrant or in the second quadrant.

State, true or false:
The origin (0, 0) lies on the x-axis.

State, true or false:
The point (a, b) lies on the y-axis if b = 0.

In 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:
3 - 2x = 7; 2y + 1 = 10 - 2`(1)/(2)`y.

In the following, find the co-ordinates of the point whose abscissa is the solution of the first equation and ordinate is the solution of the second equation:
`(2"a")/(3) - 1 = "a"/(2); (15 - 4"b")/(7) = (2"b" - 1)/(3)`.

In the following, find the co-ordinates of the point whose abscissa is the solution of the first equation and ordinate is the solution of the second equation:
`5x - (5 - x) = (1)/(2) (3 - x); 4 -3y = (4 + y)/(3)`

In the following, the coordinates of the three vertices of a rectangle ABCD are given. By plotting the given points; find, in case, the coordinates of the fourth vertex:
A(2, 0), B(8, 0) and C(8, 4).

In the following, the coordinates of the three vertices of a rectangle ABCD are given. By plotting the given points; find, in case, the coordinates of the fourth vertex:
A (4, 2), B(-2, 2) and D(4, -2).

In the following, the coordinates of the three vertices of a rectangle ABCD are given. By plotting the given points; find, in case, the coordinates of the fourth vertex:
A (- 4, - 6), C(6, 0) and D(- 4, 0).

In the following, the coordinates of the three vertices of a rectangle ABCD are given. By plotting the given points; find, in case, the coordinates of the fourth vertex:
B (10, 4), C(0, 4) and D(0, -2).

A (−2, 2), B(8, 2) and C(4, −4) are the vertices of a parallelogram ABCD. By plotting the given points on a graph paper, find the coordinates of the fourth vertex D.

Also, form the same graph, state the co-ordinates of the mid-points of the sides AB and CD.

A (-2, 4), C(4, 10) and D(-2, 10) are the vertices of a square ABCD. Use the graphical method to find the co-ordinates of the fourth vertex B. Also, find:
(i) The co-ordinates of the mid-point of BC;
(ii) The co-ordinates of the mid-point of CD and
(iii) The co-ordinates of the point of intersection of the diagonals of the square ABCD.

Line y + 7 = 0 is ______.

A line is parallel to y-axis and at a distance of 5 units on the positive side of the x-axis. The equation of the line is ______.

6x − 5y = 7 is the equation of a line. If x = 2 then the value of y will be ______.

For equation `x/3 - y/2` = 1, the value of y for x = 9 is ______.

Lines x − 4 = 0 and 3y = 1 intersect each other at point P. The co-ordinates of point P are ______.

Draw the graph for the linear equation given below:
x = 3

Draw the graph for the linear equation given below:
x + 3 = 0

Draw the graph for the linear equation given below:
x - 5 = 0

Draw the graph for the linear equation given below:
2x - 7 = 0

Draw the graph for the linear equation given below:
y = 4

Draw the graph for the linear equation given below:
y + 6 = 0

Draw the graph for the linear equation given below:
y - 2 = 0

Draw the graph for the linear equation given below:

3y + 5 = 0

Draw the graph for the linear equation given below:
2y - 5 = 0

Draw the graph for the linear equation given below:
y = 0

Draw the graph for the linear equation given below:
x = 0

Draw the graph for the linear equation given below:
y = 3x

Draw the graph for the linear equation given below:
y = - x

Draw the graph for the linear equation given below:
y = - 2x

Draw the graph for the linear equation given below:
y = x

Draw the graph for the linear equation given below:
5x+ y = 0.

Draw the graph for the linear equation given below:
x + 2y = 0

Draw the graph for the linear equation given below:
4x - y = 0

Draw the graph for the linear equation given below:
3x + 2y = 0

Draw the graph for the linear equation given below:
x = - 2y

Draw the graph for the linear equation given below:

y = 2x + 3

Draw the graph for the linear equation given below:
y = `(2x)/(3) - 1`

Draw the graph for the linear equation given below:
y = - x + 4

Draw the graph for the linear equation given below:
y = `4x - (5)/(2)`

Draw the graph for the each linear equation given below:
y = `(3x)/(2) + (2)/(3)`

Draw the graph for the linear equation given below:
2x - 3y = 4

Draw the graph for the linear equation given below:
`(x - 1)/(3) - (y + 2)/(2) = 0`

Draw the graph for the linear equation given below:
x - 3 = `(2)/(5)(y + 1)`

Draw the graph for the linear equation given below:
x + 5y + 2 = 0

Draw the graph for the equation given below:
3x + 2y = 6

Draw the graph for the equation given below:
2x - 5y = 10

Draw the graph for the equation given below:
`(1)/(2) x + (2)/(3) y = 5`.

Draw the graph for the equation given below:

`(2x - 1)/(3) - (y - 2)/(5) = 0`

For the linear equation, given above, draw the graph and then use the graph drawn (in the following case) to find the area of a triangle enclosed by the graph and the co-ordinates axes:

3x − (5 − y) = 7

For the linear equation, given above, draw the graph and then use the graph drawn (in the following case) to find the area of a triangle enclosed by the graph and the co-ordinates axes:

7 - 3 (1 - y) = -5 + 2x

For the pair of linear equations given below, draw graphs and then state, whether the lines drawn are parallel or perpendicular to each other.
y = 3x - 1
y = 3x + 2

For the pair of linear equations given below, draw graphs and then state, whether the lines drawn are parallel or perpendicular to each other.
y = x - 3
y = - x + 5

For the pair of linear equations given below, draw graphs and then state, whether the lines drawn are parallel or perpendicular to each other.
2x - 3y = 6
`x/(2) + y/(3) = 1`

For the pair of linear equations given below, draw graphs and then state, whether the lines drawn are parallel or perpendicular to each other.
3x + 4y = 24
`x/(4) + y/(3) = 1`

On the same graph paper, plot the graph of y = x - 2, y = 2x + 1 and y = 4 from x= - 4 to 3.

On the same graph paper, plot the graphs of y = 2x - 1, y = 2x and y = 2x + 1 from x = - 2 to x = 4. Are the graphs (lines) drawn parallel to each other?

The graph of 3x + 2y = 6 meets the x=axis at point P and the y-axis at point Q. Use the graphical method to find the co-ordinates of points P and Q.

The inclination of a line is 60°. The slope of the line is ______.

For the equation 2x − 5y = 8; slope is ______.

For the equation 5x − 6y = 9, the 2x y-intercept is ______.

If the slope of a line is −2 and its y-intercept is −7, the equation of the line is ______.

For the equation x − y + 1 = 0; the values of slope (m) and y-intercept (c) are ______.

In the following, find the inclination of line AB:

In the following, find the inclination of line AB:

In the following, find the inclination of line AB:

Write the inclination of a line which is: Parallel to the x-axis.

Write the inclination of a line which is: Perpendicular to the x-axis.

Write the inclination of a line which is: Parallel to the y-axis.

Write the inclination of a line which is: Perpendicular to the y-axis.

Write the slope of the line whose inclination is: 0°.

Write the slope of the line whose inclination is: 30°

Write the slope of the line whose inclination is: 45°.

Write the slope of the line whose inclination is: 60°

Find the inclination of the line whose slope is: 0

Find the inclination of the line whose slope is: 1

Find the inclination of the line whose slope is: `sqrt(3)`

Find the inclination of the line whose slope is `1/sqrt3`.

Write the slope of the line which is: Parallel to the x-axis.

Write the slope of the line which is: Perpendicular to the x-axis.

Write the slope of the line which is: Parallel to the y-axis.

Write the slope of the line which is: Perpendicular to the y-axis.

For the equation given below, find the slope and the y-intercept:
x + 3y + 5 = 0

For the equation given below, find the slope and the y-intercept:
3x - y - 8 = 0

For the equation given below, find the slope and the y-intercept:
5x = 4y + 7

For the equation given below, find the slope and the y-intercept:
x= 5y - 4

For the equation given below, find the slope and the y-intercept:
y = 7x - 2

For the equation given below, find the slope and the y-intercept:
3y = 7

For the equation given below, find the slope and the y-intercept:
4y + 9 = 0

Find the equation of the line whose:
Slope = 2 and y-intercept = 3

Find the equation of the line whose:
Slope = 5 and y-intercept = - 8

Find the equation of the line whose:
slope = - 4 and y-intercept = 2

Find the equation of the line whose:
slope = - 3 and y-intercept = - 1

Find the equation of the line whose:
slope = 0 and y-intercept = - 5

Find the equation of the line whose:
slope = 0 and y-intercept = 0

Draw the line 3x + 4y = 12 on a graph paper. From the graph paper, read the y-intercept of the line.

Draw the line 2x - 3y - 18 = 0 on a graph paper. From the graph paper, read the y-intercept of the line.

For point P(−5, 4) ______.

If the perpendicular distance of a point P from the x-axis is 5 unit then the point P has ______.

A point lies on y-axis at a distance of 2 unit from x-axis. Its co-ordinates are ______.

Three vertices of a square ABCD are A(2, 0), B(−3, 0) and C(−3, −5). Its fourth vertex D is ______.

Statement (1): In the given diagram, OAB is an equilateral triangle. Co-ordinates of the vertex B = (4, 4).

Statement (2): B = (4, `4sqrt3`)

Statement (1): The vertex B of square OABC with each side 4 units lies in fourth quadrant and its sides are along the co-ordinate axes. The co-ordinates of vertex B are (4, −4).

Statement (2): B = (4, 4).

Assertion (A): PQR is an equilateral triangle. The co-ordinates of point Q are (0, `2sqrt2`).

Reason (R): In ΔOPQ, OQ² = PQ² − OP² = 4² − 2² = 12.

Assertion (A): (2x − 3у, 8) = (2, x + 2y) ⇒ x = 1 and y = −2.

Reason (R): 2x − 3y = 2 and 8 = x + 2y which on solving give x = 4 and y = 2.

By plotting the following points on the same graph paper. Check whether they are collinear or not:
(i) (3, 5), (1, 1) and (0, -1)
(ii) (-2, -1), (-1, -4) and (-4, 1)

Plot point A(5, -7). From point A, draw AM perpendicular to the x-axis and AN perpendicular to the y-axis. Write the coordinates of points M and N.

In square ABCD; A = (3, 4), B = (-2, 4) and C = (-2, -1). By plotting these points on a graph paper, find the co-ordinates of vertex D. Also, find the area of the square.

In rectangle OABC; point O is the origin, OA = 10 units along x-axis and AB = 8 units. Find the co-ordinates of vertices A, B and C.

Draw the graph of equation x + 2y - 3 = 0. From the graph, find:
(i) x₁, the value of x, when y = 3
(ii) x₂, the value of x, when y = - 2.

Draw the graph of equation 3x – 4y = 12. Use the graph drawn to find:

1. y₁, the value of y, when x = 4.
2. y₂, the value of y, when x = 0.

Draw the graph of equation `x/(4) + y/(5) = 1` Use the graph drawn to find:
(i) x₁, the value of x, when y = 10
(ii) y₁, the value of y, when x = 8.

Use the graphical method to show that the straight lines given by the equations x + y = 2, x - 2y = 5 and `x/(3) + y = 0` pass through the same point.

Draw the graph of the line x + y = 5. Use the graph paper drawn to find the inclination and the y-intercept of the line.

Draw the graph of line 2x + y = 5.

Draw the graph of line 4x − y = 5. Use this graph to find:

1. x₁, the value of x when y = 3.
2. y₁, the value of y, when x = 3.