Posted by **Mark** on Tuesday, February 12, 2013 at 11:25am.

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?

- Math -
**Reiny**, Tuesday, February 12, 2013 at 12:14pm
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)

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