Question

consider quadrilateral abcd with vertices at coordinates a (6, 3), b (6, 9), c (9, 9), and d (9, 3) plotted on the grid below. use a grid to plot the images of a, b, c, and d after the following sequence of transformations: reflect quadrilateral abcd across the x - axis then, rotate it 180° about the origin what are the coordinates of the points after the transformation? note: do not use any spaces in your answer. a: b: c: d:

Explanation:

Step1: Reflect across x - axis

The rule for reflecting a point $(x,y)$ across the x - axis is $(x,-y)$.
For point A(6,3), after reflection across the x - axis, it becomes A1(6, - 3).
For point B(6,9), after reflection across the x - axis, it becomes B1(6, - 9).
For point C(9,9), after reflection across the x - axis, it becomes C1(9, - 9).
For point D(9,3), after reflection across the x - axis, it becomes D1(9, - 3).

Step2: Rotate 180° about the origin

The rule for rotating a point $(x,y)$ 180° about the origin is $(-x,-y)$.
For A1(6, - 3), after rotation, A'(-6,3).
For B1(6, - 9), after rotation, B'(-6,9).
For C1(9, - 9), after rotation, C'(-9,9).
For D1(9, - 3), after rotation, D'(-9,3).

Answer:

A':(-6,3)
B':(-6,9)
C':(-9,9)
D':(-9,3)