Question

The point (3,-5) is successively reflected across the x-axis, then y-axis and then x-axis again. What is the area of the rectangle formed by these 4 points?

Answer 1

Reflection over the x-axis transforms the point (x,y) into (x, -y), then

(3, -5) → (3, 5)

Reflection over the y-axis transforms the point (x,y) into (-x, y), then

(3, 5) → (-3, 5)

Reflecting this point over the x-axis,

(-3, 5) → (-3, -5)

So, the points that make the rectangle are (3, -5), (3, 5), (-3, 5), and (-3, -5)

The length of the rectangle is: 3 - (-3) = 6

The height of the rectangle is: 5 - (-5) = 10

The area of the rectangle is: length*height = 6*10 = 60