Question

rhombus wxyz with vertices w(2, - 4), x(6, - 2), y(10, - 4), and z(6, - 6): k = 3/2

Explanation:

Step1: Multiply x - coordinate by \(k\)

For a dilation with scale factor \(k=\frac{3}{2}\), if a point has coordinates \((x,y)\), the new \(x\) - coordinate of the dilated point \((x',y')\) is \(x'=\frac{3}{2}x\).
For point \(W(2,-4)\): \(x'_W=\frac{3}{2}\times2 = 3\)
For point \(X(6,-2)\): \(x'_X=\frac{3}{2}\times6=9\)
For point \(Y(10,-4)\): \(x'_Y=\frac{3}{2}\times10 = 15\)
For point \(Z(6,-6)\): \(x'_Z=\frac{3}{2}\times6=9\)

Step2: Multiply y - coordinate by \(k\)

The new \(y\) - coordinate of the dilated point \((x',y')\) is \(y'=\frac{3}{2}y\).
For point \(W(2,-4)\): \(y'_W=\frac{3}{2}\times(-4)=-6\)
For point \(X(6,-2)\): \(y'_X=\frac{3}{2}\times(-2)=-3\)
For point \(Y(10,-4)\): \(y'_Y=\frac{3}{2}\times(-4)=-6\)
For point \(Z(6,-6)\): \(y'_Z=\frac{3}{2}\times(-6)=-9\)

Answer:

\(W'(3,-6)\), \(X'(9,-3)\), \(Y'(15,-6)\), \(Z'(9,-9)\)