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: Calculate the scale factor for x - coordinate and y - coordinate

For the x - coordinate: Let the scale factor be \(k\). We know that if the original x - coordinate is \(x = 1\) and the new x - coordinate is \(x'=3\), then \(x'=k\times x\). So \(k=\frac{x'}{x}=\frac{3}{1}=3\).
For the y - coordinate: The original y - coordinate is \(y=-2\) and the new y - coordinate is \(y'=-6\). Then \(y'=k\times y\), and \(k = \frac{y'}{y}=\frac{-6}{-2}=3\).

Answer:

\((3x,3y)\)