Question

1. how does reflecting a figure over the x-axis affect its coordinates?a. the x-coordinates change sign.b. the y-coordinates change sign.c. both coordinates change sign.d. the y-coordinates remain unchanged.2. if triangle a and b are congruent, what is the length of the missing side bc?a. 1.41b. 3.61c. 4.12d. 3.00

Explanation:

Step1: Answer reflection question

When reflecting a point $(x,y)$ over the x-axis, the transformation rule is $(x,y)
ightarrow(x,-y)$, so only the y-coordinate sign flips.

Step2: Identify side for congruence

Triangles A and B are congruent, so corresponding sides are equal. We calculate the length of side BC in Triangle A, which corresponds to B'C' in Triangle B.

Step3: Calculate length of BC

Coordinates of B: $(-6,7)$, Coordinates of C: $(-6,4)$. Use distance formula:

$$ d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} $$

$$ d=\sqrt{(-6-(-6))^2+(4-7)^2}=\sqrt{0^2+(-3)^2}=\sqrt{9}=3 $$

Step4: Match to congruent side

Since $\overline{BC} \cong \overline{B'C'}$, the length of B'C' is 3.00.

Answer:

1. b. The y-coordinates change sign.
2. d. 3.00