Coordinate Geometry Practice 3: Shape Problems and Validation

Section A: Shapes on the Plane

Question 1mcq

Points

A(0,0)

,

B(4,0)

,

C(4,3)

and

D(0,3)

form which quadrilateral?

A.Square

B.Rectangle

C.Rhombus but not rectangle

D.Trapezium only

Question 2mcq

For

A(1,2)

,

B(5,2)

,

C(5,6)

and

D(1,6)

, which statement is true?

A.It is a square.

B.It is a rectangle but not a square.

C.The points are collinear.

D.It is not a quadrilateral.

Question 3mcq

A park has corners

A(0,0)

,

B(6,0)

,

C(6,8)

and

D(0,8)

. What is the diagonal length?

A.

8

B.

10

C.

12

D.

14

Question 4mcq

Before accepting a calculated distance between

(1,1)

and

(4,5)

as

10

, which estimate should raise doubt?

A.The coordinate changes are

3

and

4

, so distance should be about

5

.

B.The points are in the same quadrant.

C.Both coordinates are positive.

D.The distance formula always gives

10

.

Question 5mcq

A plotted point appears halfway between

(0,0)

and

(8,4)

. Which coordinate is most reasonable?

A.

(2,1)

B.

(4,2)

C.

(6,3)

D.

(8,4)

Section B: Diagnose and Validate

Question 6mcq

A student says

A(1,1)

,

B(2,3)

and

C(3,5)

are not collinear because the coordinates are different. What is wrong?

A.Different points can still lie on the same line.

B.Collinear points must be equal.

C.Only points on axes can be collinear.

D.The

x

-coordinates must be zero.

Question 7mcq

Point

A(3,4)

is

5

units from the origin. Which point is also

5

units from the origin?

A.

(5,5)

B.

(0,5)

C.

(4,4)

D.

(6,0)

Question 8mcq

A road segment joins

A(2,2)

and

B(14,8)

. A bus stop divides it in the ratio

1:3

from

A

to

B

. Where is the bus stop?

A.

(5,3.5)

B.

(8,5)

C.

(11,6.5)

D.

(4,4)

Question 9mcq

If distances among three points are

5

,

5

, and

8

, what type of triangle is formed?

A.Equilateral

B.Isosceles

C.Scalene

D.Right only

Question 10mcq

A student gets midpoint of

(2,8)

and

(6,4)

as

(8,12)

. What mistake was likely made?

A.Added coordinates but did not divide by

2

.

B.Subtracted coordinates instead of adding.

C.Used distance formula correctly.

D.Divided only the

x

-coordinates by

2

.