Free Coordinate Geometry 01 Practice Test - 9th Grade 

Question 1

In which quadrant does the point (-101, -299) lie?

A.

I quadrant.

B.

II quadrant.

C.

III quadrant.

D.

IV quadrant.

SOLUTION

Solution : C

(-101,-299) has -101 < 0 and -299 < 0.
We know that if abscissa < 0 and ordinate < 0 then, the point lies in third quadrant. 
Therefore (-101,-299) lies in third quadrant.

Question 2

For x = 3, y = 2, u = -9, v = 13 the point (x+y, u+v) lies in which quadrant?

A.

III quadrant

B.

II quadrant

C.

IV quadrant

D.

I quadrant

SOLUTION

Solution : D

Abscissa is x + y = 3 + 2 = 5

Ordinate is u + v = -9 + 13 = 4

The point is (5, 4).

Since both coordinates are positive the point lies in I quadrant.

Question 3

Mirror image of point (1, 2) with respect to the y-axis is ______.

A.

(1, -2)

B.

(-1, 2)

C.

(-1, -2)

D.

(0, 2)

SOLUTION

Solution : B

Mirror image of the point (1, 2) with respect to the y-axis is (-1, 2).

Question 4

A point with both of its coordinates positive lies in which quadrant?

A.

Quadrant I

B.

Quadrant II

C.

Quadrant III

D.

Quadrant IV

SOLUTION

Solution : A

If x>0 and y>0 i.e. both x and y are positive then the point lies in the first quadrant.

Question 5

The perpendicular bisector of a line segment AB passes through the origin. If the coordinates of A are (-2, 0) then the distance of point B from the origin is ___ units.

SOLUTION

Solution :

The perpendicular bisector bisects the line AB at (0, 0). The given point A (-2, 0) lies on the negative side of the origin so point B lies on the positive side of the origin with coordinates, (2, 0). Hence, the distance from the y-axis on either side of the origin should be same, i.e., 2 units.

Question 6

Which of the following points lie on the y-axis?

A.

(2, 0)

B.

(0, -4) 

C.

(5, -1)

D.

(-4, 0)

SOLUTION

Solution : B

The abscissa of the points which lie on the y-axis is 0. Therefore, the points which lie on the y-axis are represented as (0, a). Only (0,-4) satisfies the criteria.

Question 7

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

A.

0

B.

1

C.

-1

D.

Any number

SOLUTION

Solution : A

The ordinate of any point is the distance of that point from the x-axis, so the distance of any point on x-axis from the x-axis is 0. Thus all points on the x-axis are of the form (a, 0). So the value of ordinate for all points on the x-axis is 0. 

Question 8

A point is at a distance of 3 units from the x-axis and 5 units from the y-axis. Which of the following are the coordinates of the point?  

A.

(5, 3)  

B.

(–5, 3)     

C.

(–3, –5)     

D.

(3, 5)

SOLUTION

Solution : A and B

The perpendicular distance of the point from y-axis measured along the x-axis is abscissa of the point. Here 5 is the abscissa of the point.

The perpendicular distance of the point from x-axis measured along the y-axis is ordinate of the point. Here 3 is the ordinate of the point.

On the coordinate plane, points are written in the form of (abscissa, ordinate).

Since the direction is not mentioned, both (5,3) and (-5,3) are possible.

Question 9

X(6, 0), Y(-10, 0), Z (0, 0) are collinear.  

A.

True

B.

False

SOLUTION

Solution : A

Points which lie on the same line are said to be collinear. The points X(6, 0), Y(-10, 0), Z (0, 0) all lie on the X-axis and hence they are collinear.

Question 10

The distance of a point (0, –3) from the origin is

A.

0 units

B.

-3 units

C.

can't be determined

D.

3 units

SOLUTION

Solution : D

The point (0, -3) lies on the y-axis and 3 units below the x-axis. Distance is always positive so it will be counted as 3 units not -3 units. 

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