Question

the quadrilateral shown below is dilated with the center of dilation at the origin, using a scale factor of 5. then the resulting quadrilateral is translated 3 units down. after these two transformations, what are the coordinates of point a? a(\square, \square) calculator (and the coordinate plane image with point a)

Explanation:

Step1: Find original coordinates of A

From the graph, point A has coordinates \((-8, -6)\).

Step2: Apply dilation (scale factor 5)

For a dilation with center at the origin and scale factor \(k\), the new coordinates \((x', y')\) are given by \(x' = kx\) and \(y' = ky\). Here, \(k = 5\), so:
\(x' = 5\times(-8)= -40\)
\(y' = 5\times(-6)= -30\)
After dilation, the coordinates are \((-40, -30)\).

Step3: Apply translation (3 units down)

Translating 3 units down means subtracting 3 from the y - coordinate. So the new y - coordinate is \(-30-3=-33\), and the x - coordinate remains \(-40\).

Answer:

\(A'(-40, -33)\)