Question

AABC is mapped to AA'B'C using each of the following rules. Which
rule would result in AABC being NOT congruent to AA'B'C'?

A 2,y) → 2x, 2y)
B (x, y) + (-2, - y)
C (x, y) + (x+4, y – 2)
D (x, y) + (y; – x)

Answer 1

The rule which would result Δ ABC being NOT congruent to Δ A'B'C' is (x , y) → (2x , 2y) ⇒ A

Step-by-step explanation:

If a polygon is dilated around the origin by a scale factor k, then

• The rule of dilation for each vertex is (x , y) → (kx , ky)
• The polygon and its image will be similar polygons

∵ Δ ABC is mapped to Δ A'B'C'

∵ Δ ABC is not congruent to Δ A'B'C'

∵ There are three main types of congruence transformations,

   reflections, rotations, and translations

∴ Δ ABC is mapped to Δ A'B'C' by dilation

Let us check the answers

A. (x , y) → (2x , 2y)

∵ Each coordinate multiply by 2

∴ Δ ABC is dilated around the origin by scale factor 2

∴ Δ ABC is not congruent to Δ A'B'C'

B. (x , y) → (-x , -y)

∵ The sign of the two coordinates are changed

∴ Δ ABC rotated 180° around the origin

∴ Δ ABC is congruent to Δ A'B'C'

C. (x , y) → (x + 4 , y - 2)

∵ x-coordinates add by 4 and y-coordinate is subtracted by 2

∴ Δ ABC is translated 4 units right and 2 units down

∴ Δ ABC is congruent to Δ A'B'C'

D. (x , y) → (y , -x)

∵ The sign of x-coordinate is changed and the two coordinates

   are switched

∴ Δ ABC is rotated 90° clockwise around the origin

∴ Δ ABC is congruent to Δ A'B'C'

∵ Δ ABC is NOT congruent to Δ A'B'C'

∴ Answers B, C and D are not true

∴ Answer A is true

The rule which would result Δ ABC being NOT congruent to Δ A'B'C' is (x , y) → (2x , 2y)

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