Question

The sides of the triangle at right are formed by the graphs of 3x+ 2y = 1, y = x − 2, and −4x+ 9y = 22. Is the triangle isosceles? How do you know?

Answer 1

A rather lengthy question, let's find the intersection points.
1st and 2nd line:
3x+2y=1
3x+2(x-2) = 1
5x = 5
x=1 , then y = 1-2 = -1 ----> point A(1,-1)

2nd and 3rd:
4x - 9y = -22
4x - 9(x-2) = -22
-5x = -40
x = 8 , then y = 2-8 = -6 ----> point B(5,-6)

1st and 3rd:
#1 times 4 --> 12 + 8y = 4
#3 times 3 --> -12x + 27y = 66
add them
35y = 70
y = 2, then
3x + 4 = 1
x = -1 --------> point C(-1,2)

AB = √((5-1)^2 + (-6+1)^2) = √41
AC = √(-1-1)^2 + (2+1)^2) = √13
BC = √((5+1)^2 + (2+6)^2) = √100 = 10

so what is your verdict?

(check my arithmetic)

Answer 2

Well, you copied 5 and 8 wrong from the 2nd and 3rd problem to the final calculation.