Question

Square ABCD is located on a coordinate plane. The coordinates for three of the vertices are listed below.

~A(2,7)
~C(8,1)
~D(2,1)
Square ABCD is dilated by a scale factor of 2 with the center of dilation at the origin, to form square A’ B’ C’ D’. What are the coordinates of vertex B’? Explain how you determined your answer.

Answer 1

B'(16,14)

Explanation:

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Answer 2

B'(16,14)

Explanation:

First find the coordinates of the vertex B. The center of the square M is the midpoint of the diagonal AC. Since A(2,7) and C(8,1), the center has coordinates

`M\left((2+8)/(2),(7+1)/(2)\right)=M(5,4).`

Point M is also the midpoint of the diagonal BD. Let B has coordinates (x,y), then

`(x+2)/(2)=5\Rightarrow x=8,\\ \\(y+1)/(2)=4\Rightarrow y=7.`

Hence, B(8,7).

Now, the dilation by a scale factor 2 with the center of dilation at the origin has the rule

(x,y)→(2x,2y).

Thus,

B(8,7)→B'(16,14).