Question

look at the coordinate grid below showing rectangle abcd. if rectangle abcd is dilated using the origin as the center of dilation with a scale factor of 2.5, what are the coordinates of vertex c after the dilation?

Explanation:

Step1: Identify coordinates of C

From the grid, C has coordinates (7, 5).

Step2: Apply dilation formula

For dilation with center at origin and scale - factor \(k = 2.5\), if a point \((x,y)\) is dilated, the new coordinates \((x',y')\) are given by \(x'=k\times x\) and \(y'=k\times y\). Here \(x = 7\), \(y = 5\), and \(k = 2.5\). So \(x'=2.5\times7 = 17.5\) and \(y'=2.5\times5=12.5\).

Answer:

\((17.5,12.5)\)