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?
a (4, - 5)
b (-5, 4)
c (4, - 6)
d (-6, 4)

Explanation:

Step1: Find the original coordinates of point \(C\)

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

Step2: Apply the dilation formula

When a point \((x,y)\) is dilated by a factor \(k\) with the origin \((0,0)\) as the center of dilation, the new coordinates \((x',y')\) are given by the formula \(x' = kx\) and \(y'=ky\). Here \(k = 2\), \(x = 2\), \(y=-3\).
So \(x'=2\times2 = 4\) and \(y'=2\times(-3)=-6\)

Answer:

C. \((4,-6)\)