Translate triangle ABC Up 3 and right 2 then a reflection over the x-axis

Answer 1

To translate triangle ABC up 3 and to the right 2, we can add 3 to the y-coordinates of each vertex and add 2 to the x-coordinates of each vertex.

Let's say the original coordinates of triangle ABC are:
A = (x₁, y₁)
B = (x₂, y₂)
C = (x₃, y₃)

After translating up 3 and right 2, the new coordinates become:
A' = (x₁ + 2, y₁ + 3)
B' = (x₂ + 2, y₂ + 3)
C' = (x₃ + 2, y₃ + 3)

Now, to reflect the translated triangle over the x-axis, we will negate the y-coordinates of each vertex.

The final coordinates of the reflected triangle are:
A'' = (x₁ + 2, -(y₁ + 3))
B'' = (x₂ + 2, -(y₂ + 3))
C'' = (x₃ + 2, -(y₃ + 3))

Therefore, triangle ABC translated up 3 and right 2 then reflected over the x-axis can be represented by triangle A''B''C''.