# Free Coordinate Geometry 03 Practice Test - 9th Grade

What is the perpendicular distance of the point Q (5, 7) from the y-axis?

A.

5 units

B.

7 units

C.

2 units

D.

12 units

#### SOLUTION

Solution : A

The perpendicular distance of the point from y-axis measured along positive x-axis is abscissa of the point. So, the answer will be 5.

What are the coordinates of a point on the Y-axis and at a distance of 5 units in the negative direction of y-axis?

A.

(0, 5)

B.

(0,-5)

C.

(5, 0)

D.

(-5, 0)

#### SOLUTION

Solution : B

The abscissa of a point lying on the y-axis is 0 and the point on the negative y-axis has a negative ordinate, therefore, the point is (0, -5).

In which quadrant would the coordinates of any point have their abscissae and ordinates with the same signs?

A.

B.

C.

D.

#### SOLUTION

Solution : A and C

In the first and the third quadrants, the coordinates of any point would have the same signs. If a point lies in the first quadrant, its coordinates would be positive whereas if a point lies in the third quadrant, they would be negative.

Abscissa of a point is positive in __________ .

A.

B.

C.

D.

#### SOLUTION

Solution : D

Distance of a point from y-axis is called abscissa.
In order to have positive values of abscissa, the x-values should be positive.

A rectangle whose length and breadth are 5 and 3 units respectively, has a vertex at the origin. The longer side lies on the x-axis and one of the vertices lies in the first quadrant. What are the coordinates of the vertices?

A.

(0,0); (0,5); (5,3); (3,5)

B.

(0,0); (5,0); (5,3); (0,3)

C.

(0,0); (0,5); (5,3); (3,0)

D.

(0,0); (0,3); (5,3); (3,5)

#### SOLUTION

Solution : B

The coordinates of point A is (0, 0), the longer side lies on the x-axis, therefore, moving 5 units right of the origin, the coordinate of point B is (5, 0).
The breadth of the rectangle is 3 units, so moving towards the y axis from origin by 3 units, the coordinates of D will be (0,3).
Joining all the points, the coordinates of C is (5,3).

If the coordinates of the origin are (a, b), then the value of ab is ___.

#### SOLUTION

Solution :

Coordinates of the origin are (0, 0). Therefore the value of a = 0 and b = 0. So, the value of ab is 0 × 0 = 0.

The ordinate of all points on the x-axis is ___.

#### SOLUTION

Solution :

Any point on the x-axis is of the form (x, 0). So, any point on the x-axis has an ordinate 0.

The point of intersection of axes is __.

#### SOLUTION

Solution :

Point of intersection of axes is called Origin.

If any point P(x,y) is in the II Quadrant then the value of x is ___ and the value of y is positive.

#### SOLUTION

Solution :

In the II Quadrant, the value of x is negative and the value of y is positive.

Any point on x- axis is in the form (a, 0).

A.

True

B.

False

#### SOLUTION

Solution : A

Any point on x- axis is in the form (a, 0).