Question

I will give the Brainliest answer! PLEASE HELP! The vertices of a triangle are located at the points A (1,1) , B (2,3), C (5,0). The triangle is translated 4 units down, then reflected across the x-axis to obtain triangle A'B'C'. What are the coordinates of the vertices of triangle A'B'C'?

Answer 1

1.
The first transformation, the translation 4 units down, can be described with the following symbols:

(x, y) → (x, y-4).

as the points are shifted 4 units vertically, down. Thus the x-coordinates of the points do not change.

A'(1, 1) → A"(1, 1-4)=A"(1, -3).
B'(2, 3) → B"(2, 3-4)=B"(2, -1).
C'(5, 0) → C"(5, 0-4)=C"(5, -4).

2.
The second transformation can be described with:

(x, y) → (x, -y). 

as a reflection with respect to the x-axis maps:

for example, (5, -7) to (5, 7), or (-3, -4) to (-3, 4)


thus, under this transformation A", B", C" are mapped to A', B' and C' as follows:

A"(1, -3)→A'(1, -(-3))=A'(1, 3)
B"(2, -1)→B'(2, -(-1))=B'(2, 1)
C"(5, -4)→C'(5, -(-4))=C'(5, 4)

Answer:

A'(1, 3),  B'(2, 1),   C'(5, 4)