Question

question 6 points 4 write down the vertices of the dilation image of the square a (0, 0), b (0, 4), c (4, 4), and d (4, 0) with a scale factor of 3.

Explanation:

Step1: Recall Dilation Rule

To dilate a point \((x, y)\) with a scale factor \(k\) centered at the origin, the new coordinates are \((kx, ky)\).

Step2: Dilate Point A

For point \(A(0, 0)\), applying the dilation: \(x = 0\times3 = 0\), \(y = 0\times3 = 0\). So \(A'=(0, 0)\).

Step3: Dilate Point B

For point \(B(0, 4)\), \(x = 0\times3 = 0\), \(y = 4\times3 = 12\). So \(B'=(0, 12)\).

Step4: Dilate Point C

For point \(C(4, 4)\), \(x = 4\times3 = 12\), \(y = 4\times3 = 12\). So \(C'=(12, 12)\).

Step5: Dilate Point D

For point \(D(4, 0)\), \(x = 4\times3 = 12\), \(y = 0\times3 = 0\). So \(D'=(12, 0)\).

Answer:

The vertices of the dilation image are \(A'(0, 0)\), \(B'(0, 12)\), \(C'(12, 12)\), and \(D'(12, 0)\).