A(4, -1), B(0, 7) and C(-2, 5) are the vertices of a triangle. △ABC is reflected in the y-axis and then reflected in the origin. Find the coordinates of the final images of the vertices.

The graph for this problem is shown below:

First the triangle is reflected in y-axis.

We know that,

Rule to find reflection of a point in y-axis :

1. Change the sign of abscissa i.e. x-coordinate.
2. Retain the ordinate i.e. y-coordinate.

∴ Coordinates of
⇒ A(4, -1) on reflection in y-axis becomes A'(-4, -1).
⇒ B(0, 7) on reflection in y-axis becomes B'(0, 7).
⇒ C(-2, 5) on reflection in y-axis becomes C'(2, 5).

Now the triangle is reflected in origin.

We know that,

Rules to find the reflection of a point in the origin :

1. Change the sign of abscissa i.e. x-coordinate.
2. Change the sign of ordinate i.e. y-coordinate.

∴ Coordinates of
⇒ A'(-4, -1) on reflection in y-axis becomes A''(4, 1).
⇒ B'(0, 7) on reflection in y-axis becomes B''(0, -7).
⇒ C'(2, 5) on reflection in y-axis becomes C''(-2, -5).

Hence, the coordinates of the final images of the vertices are (4, 1), (0, -7) and (-2, -5) respectively.