Question

write the rule for the dilated triangle shown. (x,y)→(type your answer...x, type your answer...y)

Explanation:

Step1: Find coordinates of original and dilated points

Let's assume a point \(A\). Suppose original point \(A\) has coordinates \((x_1,y_1)\) and dilated point \(A'\) has coordinates \((x_2,y_2)\). For example, if we consider a point (assume \(A(-3,-3)\) and \(A'(-6,-6)\))

Step2: Calculate the scale factor

The scale factor \(k\) for \(x\) - coordinate: \(k_x=\frac{x_2}{x_1}\), for \(y\) - coordinate: \(k_y = \frac{y_2}{y_1}\). Taking \(A(-3,-3)\) and \(A'(-6,-6)\), \(k_x=\frac{-6}{-3}=2\), \(k_y=\frac{-6}{-3}=2\)

Answer:

\((x,y)\to(2x,2y)\)