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



Answer :

RedRicin
You should know that you can predict changes in coordinates after translations without a graph or anything like that.

(x, y) reflected over the x axis = (x, -y)
(x, y) reflected over the y axis = (-x, y)
(x, y) rotated 90 degrees around the origin = (y, -x)
(x, y) rotated 180 degrees around the origin = (-x, -y)
(x, y) rotated 270 degrees around the origin - (-x, y)

So here's our set of points.
A(1, 2), B(4, 6), C(4, 6)

Here's those points reflected over the x axis.
A'(1, -2), B'(4, -6), C'(4, -6)

And here's those points rotated 180° around the origin.
A''(2, -1), B''(6, -4), C''(6, -4)

I think you made a mistake writing down the question, though, because B and C are the same yet you say ABC forms a triangle. You should be able to go through this process with whatever the coordinate was supposed to be.

Answer: C

A' (-1, 2) , B' (-4, 6), C'(-4, 2)

Step-by-step explanation:

I'm not going to explain like the guy above me but I know I'm right bc teacher confirmed ✅

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