Question

dilate △def with a scale factor of 1/2.

1. what are the coordinates of d? graph the point on the coordinate plane.
2. what are the coordinates of e? graph the point on the coordinate plane.
3. what are the coordinates of f? graph the point on the coordinate plane.
4. is this an example of an enlargement or reduction?

Explanation:

Step1: Identify the original coordinates

Assume from the graph (common coordinate - plane reading), if \(D(-4,2)\), \(E(2,4)\), \(F(-2,-4)\)

Step2: Apply the dilation formula

The dilation formula is \((x,y)\to(\frac{1}{2}x,\frac{1}{2}y)\)
For point \(D\):
\(x=-4,y = 2\)
\(x'=\frac{1}{2}\times(-4)=-2\), \(y'=\frac{1}{2}\times2 = 1\)
For point \(E\):
\(x = 2,y=4\)
\(x'=\frac{1}{2}\times2=1\), \(y'=\frac{1}{2}\times4 = 2\)
For point \(F\):
\(x=-2,y=-4\)
\(x'=\frac{1}{2}\times(-2)=-1\), \(y'=\frac{1}{2}\times(-4)=-2\)

Step3: Determine enlargement or reduction

Since the scale factor \(k=\frac{1}{2}<1\)

Answer:

1. \((-2,1)\)
2. \((1,2)\)
3. \((-1,-2)\)
4. Reduction