Question

Triangle ABC is reflected over the x-axis. У C(5, - 1) | A(0, - 2) -3 -4 B(2, - 4) 5 -6 What are the vertices of AA'B'C '?

Answer 1

The vertices of the triangle A'B'C' are
`A'(x,y) =(0,2)`,
`B'(x,y) = (-2,4)` and
`C'(x,y) = (-5,1)`, respectively.

Explanation:

Vectorially speaking, the reflection of a point over the x-axis is defined by the following expression:

`P'(x,y) = P(x,y) -2\cdot P(x,y)`

`P'(x,y) = -P(x,y)` (1)

Where:

`P(x,y)` - Original point.

`P'(x,y)` - Reflected point.

If we know that
`A(x,y) = (0,-2)`,
`B(x,y) = (2,-4)` and
`C(x,y) = (5,-1)`, then the vertices of the triangle A'B'C':

`A'(x,y) =(0,2)`,
`B'(x,y) = (-2,4)`,
`C'(x,y) = (-5,1)`

The vertices of the triangle A'B'C' are
`A'(x,y) =(0,2)`,
`B'(x,y) = (-2,4)` and
`C'(x,y) = (-5,1)`, respectively.