Question

give the new coordinates for dilating rhombus wxyz with vertices w(2, -4), x(6, -2), y(10, -4), and z(6, -6): k = \frac{3}{2}
there is no picture for this question.
write the numerical answer (ie if you get 2 for your answer, type \2\ not \two\)
w ( type your answer... , type your answer... )
x ( type your answer... , type your answer... )
y ( type your answer... , type your answer... )
z ( type your answer... , type your answer... )

Explanation:

Step1: Recall Dilation Rule

To dilate a point \((x, y)\) with a scale factor \(k\) centered at the origin, the new coordinates \((x', y')\) are given by \(x' = k \cdot x\) and \(y' = k \cdot y\).

Step2: Dilate Point W(2, -4)

For \(W(2, -4)\) and \(k=\frac{3}{2}\):
\(x' = \frac{3}{2} \times 2 = 3\)
\(y' = \frac{3}{2} \times (-4) = -6\)
So, \(W'(3, -6)\)

Step3: Dilate Point X(6, -2)

For \(X(6, -2)\) and \(k=\frac{3}{2}\):
\(x' = \frac{3}{2} \times 6 = 9\)
\(y' = \frac{3}{2} \times (-2) = -3\)
So, \(X'(9, -3)\)

Step4: Dilate Point Y(10, -4)

For \(Y(10, -4)\) and \(k=\frac{3}{2}\):
\(x' = \frac{3}{2} \times 10 = 15\)
\(y' = \frac{3}{2} \times (-4) = -6\)
So, \(Y'(15, -6)\)

Step5: Dilate Point Z(6, -6)

For \(Z(6, -6)\) and \(k=\frac{3}{2}\):
\(x' = \frac{3}{2} \times 6 = 9\)
\(y' = \frac{3}{2} \times (-6) = -9\)
So, \(Z'(9, -9)\)

Answer:

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