Question

question 7 points 4
the vertices of a polygon abcd is a (1, 2), b (1, 4), c (2, 6), and d (5, 4). the polygon is dilated by a scale factor 3. find the coordinates of the dilated polygon.

Explanation:

Step1: Recall Dilation Rule

To dilate a point \((x, y)\) by a scale factor \(k\), we multiply each coordinate by \(k\), so the new point is \((kx, ky)\).

Step2: Dilate Point A

For \(A(1, 2)\) and \(k = 3\), new \(x\)-coordinate: \(1\times3 = 3\), new \(y\)-coordinate: \(2\times3 = 6\). So \(A'=(3, 6)\).

Step3: Dilate Point B

For \(B(1, 4)\) and \(k = 3\), new \(x\)-coordinate: \(1\times3 = 3\), new \(y\)-coordinate: \(4\times3 = 12\). So \(B'=(3, 12)\).

Step4: Dilate Point C

For \(C(2, 6)\) and \(k = 3\), new \(x\)-coordinate: \(2\times3 = 6\), new \(y\)-coordinate: \(6\times3 = 18\). So \(C'=(6, 18)\).

Step5: Dilate Point D

For \(D(5, 4)\) and \(k = 3\), new \(x\)-coordinate: \(5\times3 = 15\), new \(y\)-coordinate: \(4\times3 = 12\). So \(D'=(15, 12)\).

Answer:

The coordinates of the dilated polygon are \(A'(3, 6)\), \(B'(3, 12)\), \(C'(6, 18)\), and \(D'(15, 12)\).