Question

guided example 6:
write a similarity transformation that maps \\( \triangle mnp \\) to \\( \triangle fgh \\).

Explanation:

Step1: Determine the scale factor

Count the lengths of corresponding sides. For example, if \( MN = 4 \) units and \( FG=2 \) units, the scale factor \( k=\frac{FG}{MN}=\frac{2}{4}=\frac{1}{2} \).

Step2: Determine the rotation

Notice that \(\triangle MNP\) needs to be rotated \( 180^{\circ}\) about the origin. The rotation rule for a \(180^{\circ}\) rotation about the origin is \((x,y)\to(-x, -y)\).

Answer:

A similarity transformation is a rotation of \(180^{\circ}\) about the origin followed by a dilation with a scale factor of \(\frac{1}{2}\).