Question

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

Answer 1

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

$M\left(\dfrac{2+8}{2},\dfrac{7+1}{2}\right)=M(5,4).$

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

$\dfrac{x+2}{2}=5\Rightarrow x=8,\\ \\\dfrac{y+1}{2}=4\Rightarrow y=7.$

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).