Question: 11) dilation of $\frac{1}{4}$ about the origin \[ \begin{array}{c} V’ = (-2, 3) \\ U’ = (3,…

11. dilation of $\frac{1}{4}$ about the origin

\[ \begin{array}{c} V’ = (-2, 3) \\ U’ = (3, 2) \\ T’ = (0, 3) \\ W’ = (0, 3) \end{array} \]

Solution

Step 1: Recall the formula for dilation about the origin. \[ (x, y) \to \left( \frac{1}{4} x, \frac{1}{4} y \right) \] Step 2: Given the image points after dilation: \[ \begin{cases} U’ = (3, 2) & \\ V’ = (-2, 3) & \\ W’ = (0, 3) & \end{cases} \] Step 3: To find the original points, reverse the dilation by multiplying each coordinate by 4. \[ U = (4 \times 3, 4 \times 2) = (12, 8) \] & \[ V = (4 \times (-2), 4 \times 3) = (-8, 12) \] & \[ W = (4 \times 0, 4 \times 3) = (0, 12) \]