Posted by Mark on .
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,
A rather lengthy question, let's find the intersection points.
1st and 2nd line:
3x+2y=1
3x+2(x2) = 1
5x = 5
x=1 , then y = 12 = 1 > point A(1,1)
2nd and 3rd:
4x  9y = 22
4x  9(x2) = 22
5x = 40
x = 8 , then y = 28 = 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 = √((51)^2 + (6+1)^2) = √41
AC = √(11)^2 + (2+1)^2) = √13
BC = √((5+1)^2 + (2+6)^2) = √100 = 10
so what is your verdict?
(check my arithmetic) 
Math 
John,
Well, you copied 5 and 8 wrong from the 2nd and 3rd problem to the final calculation.