Question

the figure below shows rectangle abcd on a coordinate plane. if the rectangle is dilated using the rule (x, y)→(1/4x, 1/4y) with the origin as the center of dilation, what are the coordinates of vertex c of the dilated rectangle abcd? a (4, 3) b (15/4, 10/4) c (3, 4) d (10/4, 15/4)

Explanation:

Step1: Identify original coordinates of C

From the graph, the coordinates of vertex C are (16, 12).

Step2: Apply dilation rule

The dilation rule is \((x,y)\to(\frac{1}{4}x,\frac{1}{4}y)\). For \(x = 16\) and \(y=12\), we have \(x'=\frac{1}{4}\times16 = 4\) and \(y'=\frac{1}{4}\times12 = 3\).

Answer:

A. (4, 3)