Question

The vertices of a triangle are $A\left(2,\ 5\right)$ , $B\left(1,\ 2\right)$ , and $C\left(3,\ 1\right)$ . Find the coordinates of the image after a reflection in the y-axis.

Answer 1

The coordinates of the vertices of the reflected triangle are A′ (−2,5), B′ (−1,2), and C (−3,1).

When a point is reflected across the y-axis, the x-coordinate is negated while the y-coordinate remains the same.

So, for a point (x,y), its image after reflection across the y-axis is (−x,y).

Let's apply this reflection to each vertex of the triangle:

For point A(2,5), the image after reflection is (−2,5).

For point B(1,2), the image after reflection is (−1,2).

For point C(3,1), the image after reflection is (−3,1).

Therefore, the coordinates of the vertices of the reflected triangle are

A′ (−2,5), B′ (−1,2), and C (−3,1).