Triangle ABC has vertices A(0,8), B(2,0), C(8,0). A vertical line intersects AC at R and {BC} at S, forming triangle RSC. If the area of RSC is 12.5, determine the positive difference of the x and y coordinates of point R.

Guest Feb 10, 2022

#1**+1 **

Let O be the origin.

Triangle(OAC) is similar to triangle(SRC).

OA = 8 and OC = 8 making OA = OC.

Because of similar triangles, SR = SC; call this length "x".

Area(triangle(SRC)) = ½·x·x = 12.5 ---> x^{2} = 25 ---> x = 5

The distance from S to R is 5.

The distance from C to S is also 5.

Can you take it from here?

geno3141 Feb 10, 2022

#2**0 **

Yes!

so we can use the distance formula which is √ [ (x₂ - x₁)² + (y₂ - y₁)²], and plug S's coordinate in along with C, we get

S= (13,0) correct?

Guest Feb 10, 2022

#3**0 **

wait a second, that would be incorrect considering the x for S should be smaller than 8

Guest Feb 10, 2022