Question

Which statement explains why △ABC is congruent to △A′B′C′ ?

A You can map △ABC onto △A′B′C′ by reflecting it across the x-axis and then across the y-axis, which is a sequence of rigid motions.

B You can map △ABC onto △A′B′C′ by translating it 6 units left and reflecting it over the x-axis, which is a sequence of rigid motions.

C You can map △ABC onto △A′B′C′ by translating it 2 units up and reflecting it across the y-axis, which is a sequence of rigid motions.

D You can map △ABC onto △A′B′C′ reflecting it across the line y = x and rotating it 90° counterclockwise about the origin, which is a sequence of rigid motions.

Answer 1

Its B

Explanation:

Answer 2

Answer is B

Explanation:

Observing the two triangles ABC and A'B'C' we find the following.

ABC has become the new triangle by a continuous series of translations.

First the coordinates are shifted 6 units left horizontally thus making coordinates as (x-6,y) for (x,y)

Next translation is done by changing y coordinate into negative y. In other words, (x,y) which became (x-6,y) now transformed into (x-6,-y)

The second can also be interpreted as translation of reflection over the x axis.

Now we find that ABC is exactly matched into A"B'C"

Hence ABC is congruent to A"B'C"