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.

B'(16,14)

Step-by-step 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

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

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).

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step-by-step explanation: