The point A (3,4) is reflected over the x-axis to B. Then B is reflected over the line y=x to C. What is the area of triangle ABC?

Guest Sep 13, 2018

#2**+1 **

When A is reflected over the x axis to B....the new point is ( 3, -4)

Call this the base of the triangle AB = 8 units

And the equation of the line on which this base lies is x = 3

When B is reflected over the line y = x the new point C has the coordinates ( -4, 3)

The distance from this point to the line x = 3 is the height of the triangle = 7

So....the area of ABC = (1/2) AB * 7 = (1/2) (8)(7) = 28 units^2

CPhill
Sep 13, 2018