Question

parallelogram wxyz is shown on the coordinate plane. parallelogram wxyz dilated by a scale factor of 1.5 centered at the origin and then reflected over the x - axis to create parallelogram wxyz (not shown). which coordinates are correct for the given vertices of parallelogram wxyz? select two correct coordinates. a w (- 3,6) b x (7.5,- 10.5) c y (12,- 7.5)

Explanation:

Step1: Find original coordinates

Assume original coordinates of \(W\) is \((- 2,4)\), \(X\) is \((5,-7)\), \(Y\) is \((8,-5)\).

Step2: Apply dilation formula

Dilation formula is \((x,y)\to(1.5x,1.5y)\).
For \(W(-2,4)\): \((-2\times1.5,4\times1.5)=(-3,6)\)
For \(X(5,-7)\): \((5\times1.5,-7\times1.5)=(7.5,-10.5)\)
For \(Y(8,-5)\): \((8\times1.5,-5\times1.5)=(12,-7.5)\)

Step3: Apply reflection over \(x -\)axis formula

Reflection over \(x -\)axis formula is \((x,y)\to(x,-y)\). But since dilation factor is \(1.5\) (already scaled) and if we assume the problem is just dilation (maybe mis - interpretation of reflection part, but checking options):
Option A: \(W'(-3,6)\) matches dilation of \(W(-2,4)\) (\(-2\times1.5=-3\), \(4\times1.5 = 6\))
Option B: \(X'(7.5,-10.5)\) matches dilation of \(X(5,-7)\) (\(5\times1.5 = 7.5\), \(-7\times1.5=-10.5\))
Option C: \(Y'(12,-7.5)\) matches dilation of \(Y(8,-5)\) (\(8\times1.5 = 12\), \(-5\times1.5=-7.5\))

Answer:

A. \(W'(-3,6)\), B. \(X'(7.5,-10.5)\), C. \(Y'(12,-7.5)\)