Answer:
Coordinates of image: W' (-1, 5), X' (-1, 1.5), Y' (7, -2), and Z' (7, 5)
Explaining how I found the coordinates: To reflect WXYZ across the y-axis, I used the rule (x, -y), which means I changed the sign of each y-coordinate and kept the same x-coordinate. Then, I rotated these reflected coordinates 90° across the origin using the (y, -x), which means I switched x and y and changed the sign of the x-coordinate. Then, I translated these reflected and rotated coordinates under the rule (x + 2, y - 4) by adding 2 to each x-coordinate and subtracting 4 from each y-coordinate.
Explanation:
In order to prevent confusion, I'll put a 1 beside the reflected points, 1-2 when the point is reflected and rotated, and 1-2-3 when the (x + 2, y - 4) rule is applied. Then, the coordinates for the final image will have a ' beside them
Example:
W-1 = Coordinates of W point reflected across the y-axis
W-1-2 = Coordinates of W point reflected across the y-axis and rotated 90° about the origin
W-1-2-3 = Coordinates of W point reflected across the y-axis, rotated 90° about the origin, and the (x + 2, y - 4) translation rule is applied
Step 1: Reflect WXYZ across the y-axis:
- The rule for reflecting a point across the y-axis is (-x, y).
- Thus, we change the sign of the x-coordinate and keep the same y-coordinate.
Original: W (-9, 3); Reflect across y-axis: W-1 (9, 3)
Original: X (-5.5, 3); Reflect across y-axis: X-1 (5.5, 3)
Original: Y (-2, -5); Reflect across y-axis: Y-1 (2, -5)
Original: Z (-9, -5); Reflect across y-axis: Z-1 (9, -5)
Step 2: Rotate W1-X1-Y1-Z1 clockwise 90° about the origin:
- The rule for rotating a point 90° about the origin is (y, -x)
- Thus, we switch the x and y coordinates and change the sign of the x-coordinate (now in the place of the y-coordinate)
Reflected: W-1 (9, 3); Rotated: W-1-2 (-3, 9)
Reflected: X-1 (5.5, 3); Rotated: X-1-2 (-3, 5.5)
Reflected: Y-1 (2, -5); Rotated: Y-1-2 (5, 2)
Reflected: Z-1 (9, -5); Rotated: Z-1-2 (5, 9)
Step 2: Apply (x + 2, y - 4) translation rule to W12-X12-Y12-Z12
- The (x + 2, y - 4) translation rule means that we add 2 to every x-coordinate and subtract 4 from every y-coordinate.
Reflected & Rotated: W-1-2 (-3, 9); Translated: W-1-2-3 (-1, 5)
Reflected & Rotated: X-1-2 (-3, 5.5); Translated: X-1-2-3 (-1, 1.5)
Reflected & Rotated: Y-1-2 (5, 2); Translated: Y-1-2-3 (7, -2)
Reflected & Rotated: Z-1-2 (5, 9); Translated: Z-1-2-3 (7, 5)
Thus, the coordinates of trapezoid W'X'Y'Z' are:
W' (-1, 5), X' (-1, 1.5), Y' (7, -2), and Z' (7, 5)
You can use the following paragraph to explain how you got the coordinates:
To reflect WXYZ across the y-axis, I used the rule (x, -y), which means I changed the sign of each y-coordinate and kept the same x-coordinate. Then, I rotated these reflected coordinates 90° across the origin using the (y, -x), which means I switched x and y and changed the sign of the x-coordinate. Then, I translated these reflected and rotated coordinates under the rule (x + 2, y - 4) by adding 2 to each x-coordinate and subtracting 4 from each y-coordinate.