Question

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

Explanation:

Step1: Apply the scale factor formula

When a point \((x,y)\) is scaled by a factor \(k\), the new point \((x',y')\) is given by \(x'=k\times x\) and \(y' = k\times y\). Here \(k=\frac{3}{2}\).
For point \(W(2,-4)\):
\(x'_W=\frac{3}{2}\times2 = 3\)
\(y'_W=\frac{3}{2}\times(-4)=-6\)

Step2: For point \(X(6,-2)\)

\(x'_X=\frac{3}{2}\times6 = 9\)
\(y'_X=\frac{3}{2}\times(-2)=-3\)

Step3: For point \(Y(10,-4)\)

\(x'_Y=\frac{3}{2}\times10 = 15\)
\(y'_Y=\frac{3}{2}\times(-4)=-6\)

Step4: For point \(Z(6,-6)\)

\(x'_Z=\frac{3}{2}\times6 = 9\)
\(y'_Z=\frac{3}{2}\times(-6)=-9\)

Answer:

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