Question

1. graph the image of the quadrilateral below using a scale factor of ( k = 3 / 2 ).

( w ^ { prime } ( __ , __ ) )

( x ^ { prime } ( __ , __ ) )

( y ^ { prime } ( __ , __ ) )

( z ^ { prime } ( __ , __ ) )

Explanation:

Step1: Identify the original coordinates

Assume the original coordinates are \(W(1,5)\), \(X(4,6)\), \(Y(6,3)\), \(Z(3,0)\) (by observing the graph).

Step2: Apply the scale - factor formula

The formula for dilation (scaling) about the origin is \((x,y)\to(kx,ky)\) where \(k = \frac{3}{2}\).

• For point \(W(1,5)\):

\(x'=\frac{3}{2}\times1=\frac{3}{2}\), \(y'=\frac{3}{2}\times5=\frac{15}{2}\)

• For point \(X(4,6)\):

\(x'=\frac{3}{2}\times4 = 6\), \(y'=\frac{3}{2}\times6=9\)

• For point \(Y(6,3)\):

\(x'=\frac{3}{2}\times6 = 9\), \(y'=\frac{3}{2}\times3=\frac{9}{2}\)

• For point \(Z(3,0)\):

\(x'=\frac{3}{2}\times3=\frac{9}{2}\), \(y'=\frac{3}{2}\times0 = 0\)

Answer:

\(W'(\frac{3}{2},\frac{15}{2})\), \(X'(6,9)\), \(Y'(9,\frac{9}{2})\), \(Z'(\frac{9}{2},0)\)