AnswersSRC 2022 MJ Grade 8 Pre-Algebra Q1Congruence and Transformations — Unit testQuestion 7
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Congruence and Transformations — Unit test

Question 7 • SRC 2022 M/J Grade 8 Pre-Algebra Q1

Max is trying to prove to his friend that two reflections, one across the x-axis and another across the y-axis, will not result in a reflection across the line y = x for a pre-image in quadrant II. His friend Josiah is trying to prove that a reflection across the x-axis followed by a reflection across the y-axis will result in a reflection across the line y = x for a pre-image in quadrant II. Which student is correct, and which statements below will help him prove his conjecture? Select the three correct answers.

Answer
A
Max is correct.
B
Josiah is correct.
C
Taking the result from the first reflection (x, –y) and applying the second mapping rule will result in (–x, –y), not (y, x), which reflecting across the line y = x should give.
D
If one reflects a figure first across the x-axis from quadrant II then reflects across the y-axis from quadrant III, the image will end up in quadrant IV.
E
A figure that is reflected from quadrant II to quadrant IV across the line y = x will have the coordinates of (-y, x).

Explanation

Max is correct: reflecting (x, y) across the x-axis gives (x, −y), and then reflecting across the y-axis gives (−x, −y). A reflection across y = x instead gives (y, x), which is generally different, as statement C notes. For a point in quadrant II, the two axis reflections move it first to quadrant III and then to quadrant IV, as statement D says.

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