Question

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Triangle ABC has vertices at A(1, 2) B(4, 6) and C(4, 2) in the coordinate plane. The triangle will be reflected over the x-axis and then rotated 180 degrees about the origin to form ABC. What are the vertices of A'B'C'?

Answer 1

Answer:

The vertices of A'B'C are  A'(-1,2), B'(-4,6) and C'(-4,2).

Step-by-step explanation:

Triangle ABC has vertices at A(1, 2) B(4, 6) and C(4, 2).

If a figure reflected over x-axis, then

$(x,y)\rightarrow (x,-y)$

Therefore the vertices of triangle ABC after reflection over x-axis are:

$A(1,2)\rightarrow A'(1,-2)$

$B(4,6)\rightarrow B'(4,-6)$

$C(4,2)\rightarrow C'(4,-2)$

Rotation 180 degrees about the origin is defined as

$(x,y)\rightarrow (-x,-y)$

Therefore the vertices of triangle ABC after reflection over x-axis followed by rotated 180 degrees about the origin are:

$A(1,-2)\rightarrow A'(-1,2)$

$B(4,-6)\rightarrow B'(-4,6)$

$C(4,-2)\rightarrow C'(-4,2)$

Therefore the vertices of A'B'C are  A'(-1,2), B'(-4,6) and C'(-4,2).

Answer 2

Answer:

C

Step-by-step explanation:

If ur not trying to look at all that but you should