Question

dilate △mku with a scale factor of ½.

1. what are the coordinates of m? graph the point on the coordinate plane.
2. what are the coordinates of k? graph the point on the coordinate plane.
3. what are the coordinates of u? graph the point on the coordinate plane.
4. is this an example of an enlargement or reduction?

Explanation:

Step1: Find coordinates of \(M\), \(K\), \(U\)

From the graph, \(M(-1,2)\), \(K(1,6)\), \(U(5,2)\)

Step2: Apply dilation formula

The formula for dilation with scale factor \(k=\frac{1}{2}\) is \((x,y)\to(kx,ky)\)
For \(M(-1,2)\):
\(x'=\frac{1}{2}\times(-1)=-\frac{1}{2}\), \(y'=\frac{1}{2}\times2 = 1\)
For \(K(1,6)\):
\(x'=\frac{1}{2}\times1=\frac{1}{2}\), \(y'=\frac{1}{2}\times6 = 3\)
For \(U(5,2)\):
\(x'=\frac{1}{2}\times5=\frac{5}{2}\), \(y'=\frac{1}{2}\times2 = 1\)

Step3: Determine enlargement or reduction

Since scale factor \(k = \frac{1}{2}<1\), it is a reduction

Answer:

1. \((-\frac{1}{2},1)\)
2. \((\frac{1}{2},3)\)
3. \((\frac{5}{2},1)\)
4. Reduction