Question

Suppose that rectangle ABCD is dilated to A'B'C'D' using vertex B as the center and a magnitude of 2. What are the coordinates of D'?

A) (3, 4)
B) (8, 4)
C) (4, -8)
D) (4, -11)

Answer 1

D

the coordinates of B(4, 3 ) and D(4, - 4 )

BD = d - b ← position vector representation

= <4, - 4> - <4, 3> = <0, - 7>

BD' = 2BD = 2<0, - 7> = <0, - 14>

D' = (4 + 0, 3 - 14 ) = (4, - 11 ) → D

Answer 2

The correct option is D. (4, -11)

Explanation:

By looking at the diagram given :

The coordinates of B are : (4, 3 ) and D are : (4, - 4 )

Now, Using position vector representation

BD can be written as :

BD = D - B

= <4, - 4> - <4, 3>

= <0, - 7>

Now, rectangle ABCD is dilated to A'B'C'D' using vertex B as the center and a magnitude of 2.

⇒ BD' = 2 × BD

= 2 × <0, - 7>

= <0, - 14>

So, Coordinates of D' = (4 + 0, 3 - 14 )

= (4, - 11 )

Therefore, The correct option is D. (4, -11)