Question

$$(x,y) \to (2 - x, y - 5)$$ is an example of a transformation called a glide reflection.
complete the table using the rule. type your answers in the boxes.

input	output
$(4,6)$	$(quad,quad)$
$(7,2)$	$(quad,quad)$

diego claims that this glide reflection does not produce a triangle congruent to the original. is his claim correct?
$circ$ yes $circ$ no

Explanation:

Step1: Calculate x for (4,6)

$2 - 4 = -2$

Step2: Calculate y for (4,6)

$6 - 5 = 1$

Step3: Calculate x for (7,2)

$2 - 7 = -5$

Step4: Calculate y for (7,2)

$2 - 5 = -3$

Step5: Evaluate congruence claim

Glide reflections are isometries (preserve distance and shape), so the transformed triangle is congruent to the original. Thus Diego's claim is incorrect.

Answer:

1. Output for (4,6): $(-2, 1)$
2. Output for (7,2): $(-5, -3)$
3. No