Question

The point (-7, 4) is reflected over the line x= -3. Then, the result point is reflected over the line y = x. Where is the point located after both reflections?

A. (-10, 7)
B. (1, 4)
C. (4, -7)
D. (4, 1)

Answer 1

Answer: D. (4, 1)

Explanation:

When we have a reflection over a line, the perpendicular distance to that line is invariant.

Then, if we have the point

(-7, 4) and we have a reflection over the line x = -3

The distance between the x component and the line is:

I -7 - (-3)I = 4

Then the reflected point will also be at a distance of 4 units to the line x = 3, and this is at the point x = 1.

Then the new point is (1, 4)

Now we do a reflection over the line x = y.

This type of reflection just changes the x-component by the y-component, and the y-component by the x-component.

Then the new point will be (4, 1)

Then the correct option is D.