Question

Suppose the line segment whose endpoints are P(0,-4) and D(6,1) is reflected over the x-axis, and the reflected again over y=x. What are the coordinates of P” and D”?

Answer 1

P'' = (4, 0)

D'' = (-1, 6)

Explanation:

If the line segment was reflected over the x-axis, the rule would be (x, y) ---> (x, -y) and if the line segment is reflected over y = x, the rule would be, (x, y) ---> (x, y). So applying the reflection over the x-axis to P first, it would become P' = (0, 4). This is because a negative × negative = positive. And applying this to D, would make it D' = (6, -1).

Applying the reflection over y = x to P' first, all you would do is switch the x and y values around. So P'' = (4, 0), and D'' = (-1, 6).