Question

after a dilation, the coordinates of c are 3, -6. what is the dilation rule? (x + 2, y - 4) (3x, 3y) (\frac{1}{3}x, \frac{1}{3}y) (3x, -6y)

Explanation:

Step1: Find the original coordinates of point C

From the graph, the coordinates of point C are \((1,-2)\).

Step2: Determine the scale factor for x - coordinate

The x - coordinate of \(C'\) is \(3\) and the x - coordinate of \(C\) is \(1\). Let the scale factor be \(k\). Using the formula \(x'=kx\), we have \(3 = k\times1\), so \(k = 3\).

Step3: Determine the scale factor for y - coordinate

The y - coordinate of \(C'\) is \(-6\) and the y - coordinate of \(C\) is \(-2\). Using the formula \(y'=ky\), we have \(-6=k\times(-2)\), so \(k = 3\).

Answer:

\((3x,3y)\)