Answer:
The vertices of the triangle A'B'C' are [tex]A'(x,y) =(0,2)[/tex], [tex]B'(x,y) = (-2,4)[/tex] and [tex]C'(x,y) = (-5,1)[/tex], respectively.
Step-by-step explanation:
Vectorially speaking, the reflection of a point over the x-axis is defined by the following expression:
[tex]P'(x,y) = P(x,y) -2\cdot P(x,y)[/tex]
[tex]P'(x,y) = -P(x,y)[/tex] (1)
Where:
[tex]P(x,y)[/tex] - Original point.
[tex]P'(x,y)[/tex] - Reflected point.
If we know that [tex]A(x,y) = (0,-2)[/tex], [tex]B(x,y) = (2,-4)[/tex] and [tex]C(x,y) = (5,-1)[/tex], then the vertices of the triangle A'B'C':
[tex]A'(x,y) =(0,2)[/tex], [tex]B'(x,y) = (-2,4)[/tex], [tex]C'(x,y) = (-5,1)[/tex]
The vertices of the triangle A'B'C' are [tex]A'(x,y) =(0,2)[/tex], [tex]B'(x,y) = (-2,4)[/tex] and [tex]C'(x,y) = (-5,1)[/tex], respectively.
