Question

on the coordinate plane below, square (abcd) is dilated by a factor of 2, with the origin as the center of dilation, to form (abcd)
after the dilation, what is the location of (c)?

Explanation:

Step1: Find the original coordinates of point C

From the graph, we can see that the coordinates of point C are \((2, -3)\).

Step2: Apply the dilation rule

When a point \((x, y)\) is dilated by a factor of \(k\) with the origin as the center of dilation, the new coordinates \((x', y')\) are given by \(x' = kx\) and \(y' = ky\). Here, \(k = 2\), \(x = 2\), and \(y = -3\).
So, \(x' = 2\times2 = 4\) and \(y' = 2\times(-3) = -6\).

Answer:

The location of \(C'\) is \((4, -6)\)