Question

Point p is located in the first quadrant of a coordinate plane.If p is reflected across to form p',choose the four statements that will always be true.

Answer 1

When we do a reflection of a point (x, y) about a given line, the distance between the point (x, y) and the line is invariant under the transformation.

In the case of reflection over x-axis we have:

T (x, y) => (x, -y)

In the case of reflection over the y-axis, we have:

T (x, y) => (-x, y)

Because these two lines are perpendicular, a reflection over the x-axis leaves the distance between the point and the y-axis invariant (and the same for the inverse case)

Then 4 statements that will always be true:

1) The distance between p' and the x-axis is the same as the distance between p and the x-axis.

2) The distance between p' and the y-axis is the same as the distance between p and the y-axis.

From 1 and 2, we get:

3) The distance between p' and the origin is the same as the distance between p and the origin.

4) As we have a reflection, p' can not be in the same quadrant than p, then p' can not lie on the first quadrant.