Question

Which statement correctly describes the relationship between △ABC and △A′B′C′ ?

a . △ABC is congruent to △A′B′C′ because you can map △ABC to △A′B′C′ using a reflection across the y-axis, which is a rigid motion.

b . △ABC is not congruent to △A′B′C′ because there is no sequence of rigid motions that maps △ABC to △A′B′C′.

c . △ABC is congruent to △A′B′C′ because you can map △ABC to △A′B′C′ using a translation 6 units to the left, which is a rigid motion.

d . △ABC is congruent to △A′B′C′ because you can map △ABC to △A′B′C′ using a translation 6 units to the right, which is a rigid motion.

Answer 1

answer is

c . △ABC is congruent to △A′B′C′ because you can map △ABC to △A′B′C′ using a translation 6 units to the left, which is a rigid motion.

Answer 2

Left and right motion indicates change in x-value.

If we subtract 6 from the x-coordinate of each point,

A(3, 4) will be transferred to A'(3-6, 4) = A'(-3, 4).

B(4, 0) will be transferred to B'(4-6, 0) = B'(-2, 0).

C(2, 1) will be transferred to C'(2-6, 1) = C'(-4, 1).

Hence, the correct option is c. Δ ABC is congruent to Δ A'B'C' because you can mapΔ ABC to Δ A'B'C' using a translation 6 units to the left, which is a rigid motion.