Cumulative review questions

Question

a triangle has vertices A(2,4) B(6,2) and C(1,1) prove ABC is a isosceles right triangle

Answer 1

AB = sqr(2^2 +4^2) = sqr20 for A(2,4) B(6,2)

BC = sqr(5^2 +1^2) =sqr26 for B(6,2) C(1,1)

AC = sqr (1^2 +3^2) =sqr10 for A(2,4) C(1,1)

since no two sides are the same it's not isosceles

for a right triangle, sum of squares of 2 sides = square of the largest side

26 doesn't = 20+10=30, so it's not a right triangle either

it may help to plot the points, connect them and visually see it's not isosceles or right

it does form a triangle. if the points were slightly different, it could have been a right isosceles triangle