Question

write a coordinate rule for the dilation (x,y)→(□□,□□)

Explanation:

Step1: Find the scale factor

Take a point, say \(C(-0, - 4)\) and its image \(C'(0,-2)\). The scale factor \(k\) is calculated as \(k=\frac{y - coordinate\ of\ image}{y - coordinate\ of\ original}\) (since the center of dilation is the origin). For \(C\) and \(C'\), \(k=\frac{-2}{-4}=\frac{1}{2}\).

Step2: Write the coordinate rule

The general rule for dilation about the origin is \((x,y)\to(kx,ky)\). Since \(k = \frac{1}{2}\), the rule is \((x,y)\to(\frac{1}{2}x,\frac{1}{2}y)\)

Answer:

\((x,y)\to(\frac{1}{2}x,\frac{1}{2}y)\)