Question

question 13 (3 points)
triangle abc is rotated about the origin by 270° to form the triangle abc, then translated upward 10 units to form triangle abc. which of the following statements is true for δabc and δabc?
a) there isnt enough information to identify whether δabc and δabc are congruent or similar.
b) δabc and δabc are congruent triangles.
c) δabc and δabc are similar triangles.
d) δabc and δabc are neither similar nor congruent.
question 14 (5 points)
a point (3, -2) is reflected across the x - axis followed by a reflection across the y - axis. find the image of the point after the described transformations.
a) (-3, 2)
b) (3, 2)
c) (3, -2)
d) (-3, -2)

Explanation:

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Question 13

Step1: Identify transformation type

Rotation and translation are rigid motions.

Step2: Rigid motion preserves congruence

Rigid motions keep side lengths/angles equal, so $\Delta ABC \cong \Delta A''B''C''$. Congruent figures are also similar, but B is the most precise true statement.
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Question 14

Step1: Reflect across x-axis

For point $(x,y)$, reflection over x-axis: $(x, -y)$.
$(3, -2)
ightarrow (3, 2)$

Step2: Reflect across y-axis

For point $(x,y)$, reflection over y-axis: $(-x, y)$.
$(3, 2)
ightarrow (-3, 2)$

Answer:

B) $\Delta ABC$ and $\Delta A''B''C''$ are congruent triangles.
A) $(-3, 2)$