Question

Quadrilateral ABCD is dilated by a scale factor of 2 centered around (2, 2). Which statement is true about the dilation?

Answer 1

Answer:

B'D' will run through (2, 2) and will be longer than BD.

Step-by-step explanation:

The dilation with center of dilation at (2,2) by a scale factor of 2 has the rule

$(x,y)\rightarrow (2x-2,2y-2)$

Hence, the images of vertices have coordinates

• $A(1,2)\rightarrow A'(0,2);$
• $B(2,3)\rightarrow B'(2,4);$
• $C(4,2)\rightarrow C'(6,2);$
• $D(2,1)\rightarrow D'(2,0).$

Connect points A', B', C' and D' to get image quadrilateral A'B'C'D'.

Segment B'D' is twice the segment BD and passes through the center of silation, so correct option is

B'D' will run through (2, 2) and will be longer than BD.