Coordinate Geometry Final Assessment

Section A: Core Concepts

Question 1mcq

Which point lies in Quadrant IV?

A.

(3,5)

B.

(-3,5)

C.

(-3,-5)

D.

(3,-5)

Question 2mcq

If both coordinates of a point are negative, where does it lie?

A.Quadrant I

B.Quadrant II

C.Quadrant III

D.Quadrant IV

Question 3mcq

For points

(x_1,y_1)

and

(x_2,y_2)

, which expression gives the horizontal difference used in the distance formula?

A.

x_2-x_1

B.

y_2-y_1

C.

x_1+y_1

D.

x_2+y_2

Question 4mcq

Find the distance between

(2,-1)

and

(8,7)

.

A.

8

B.

9

C.

10

D.

12

Question 5mcq

Points

A(0,0)

,

B(6,0)

and

C(3,3\sqrt{3})

form which triangle?

A.Equilateral

B.Right

C.Scalene

D.Collinear

Question 6mcq

Which condition confirms that three points

A,B,C

are collinear using distances?

A.

AB+BC=AC

for one ordering

B.

AB=BC=AC

C.

AB^2+BC^2=AC^2

always

D.

AB\times BC=AC

Section B: Distance and Triangles

Question 7mcq

Point

(x,3)

is

5

units from

(0,0)

. Which equation should be solved?

A.

x^2+3^2=5^2

B.

x+3=5

C.

x^2-3^2=5

D.

3x=5

Question 8mcq

In section formula, if

P

divides

AB

in ratio

m:n

, which segment corresponds to

m:n

?

A.

AP:PB

B.

PB:AB

C.

AB:AP

D.

x:y

only

Question 9mcq

Find the point dividing

(1,1)

and

(7,13)

internally in ratio

1:2

.

A.

(3,5)

B.

(4,7)

C.

(5,9)

D.

(6,11)

Question 10mcq

Find the midpoint of

(10,-2)

and

(4,6)

.

A.

(7,2)

B.

(6,4)

C.

(14,4)

D.

(3,2)

Question 11mcq

Point

(3,0)

divides

(0,0)

and

(12,0)

in what ratio?

A.

1:3

B.

1:4

C.

3:1

D.

4:1

Question 12mcq

Which set of points forms a rectangle with sides parallel to the axes?

A.

(0,0),(5,0),(5,2),(0,2)

B.

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

C.

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

D.

(0,0),(2,2),(4,0),(2,-3)

Section C: Section Formula

Question 13mcq

A distance between

(0,0)

and

(1,1)

is reported as

4

. Which estimate shows it is unreasonable?

A.The distance should be slightly more than

1

, about

\sqrt{2}

.

B.Both coordinates are positive.

C.The points are not on the same axis.

D.The exact distance must be negative.

Question 14mcq

A point is at

(5,12)

from the origin. What is its distance from the origin?

A.

12

B.

13

C.

17

D.

25

Question 15mcq

The sides of a triangle from coordinates are found as

\sqrt{10}

,

\sqrt{10}

and

\sqrt{20}

. What type is it?

A.Equilateral

B.Isosceles right

C.Scalene

D.Collinear

Question 16mcq

Are

(1,2)

,

(3,6)

and

(5,10)

collinear?

A.Yes, all lie on

y=2x

.

B.No, the

x

-coordinates differ.

C.No, the points are in different quadrants.

D.Yes, because all coordinates are positive.

Question 17mcq

Point

(0,k)

is

7

units from

(0,0)

. Which values are possible for

k

?

A.

7

only

B.

-7

only

C.

7

or

-7

D.

0

or

7

Question 18mcq

Point

P

divides

A(4,0)

and

B(10,12)

in ratio

1:2

. Find

P

.

A.

(6,4)

B.

(8,8)

C.

(7,6)

D.

(5,3)

Section D: Applications and Checks

Question 19mcq

If the midpoint of

A(-2,4)

and

B(x,10)

is

(3,7)

, find

x

.

A.

6

B.

7

C.

8

D.

9

Question 20mcq

Point

P(6,6)

divides

A(0,0)

and

B(9,9)

. What is

AP:PB

?

A.

1:2

B.

2:1

C.

3:1

D.

1:3

Question 21mcq

A triangle has vertices

A(0,0)

,

B(8,0)

and

C(4,3)

. What is true?

A.It is isosceles.

B.It is equilateral.

C.It is collinear.

D.It has no equal sides.

Question 22mcq

When checking a coordinate answer with a rough diagram, what should you verify first?

A.Whether the point lies in the expected quadrant or between expected endpoints.

B.Whether the answer has many decimals.

C.Whether the answer is the largest option.

D.Whether the formula was memorised.

Question 23mcq

A point reflected from Quadrant II across the

x

-axis will move to which quadrant?

A.Quadrant I

B.Quadrant II

C.Quadrant III

D.Quadrant IV

Question 24mcq

Assertion: The distance formula squares coordinate differences. Reason: Squaring makes horizontal and vertical differences combine through Pythagoras. Which is correct?

A.Both are true and the reason explains the assertion.

B.Both are true but the reason does not explain it.

C.Assertion is true but reason is false.

D.Assertion is false but reason is true.