Question

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

Explanation:

Step1: Find coordinates of original points

Assume \( W(2,5) \), \( X(4,6) \), \( Y(6,3) \), \( Z(4,0) \) (by observing the graph).

Step2: Apply scale - factor formula

For a point \((x,y)\) and scale factor \(k=\frac{3}{2}\), the image point \((x',y')=(kx,ky)\).

• For \(W(2,5)\):

\(x'=\frac{3}{2}\times2 = 3\), \(y'=\frac{3}{2}\times5=\frac{15}{2}\). So \(W'(3,\frac{15}{2})\).

• For \(X(4,6)\):

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

• For \(Y(6,3)\):

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

• For \(Z(4,0)\):

\(x'=\frac{3}{2}\times4 = 6\), \(y'=\frac{3}{2}\times0 = 0\). So \(Z'(6,0)\).

Answer:

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