Is triangle ABC scalene, isosceles, or equilateral if A = (4, 6) B = (-4, 2) and C = (0, 2)? Why?
sketch it !
BC is only 4 long
the others are longer than 4 but not the same
To determine whether triangle ABC is scalene, isosceles, or equilateral, we need to compare the lengths of its sides.
First, let's find the lengths of the three sides:
1. Length of side AB:
Distance Formula: sqrt((x2 - x1)^2 + (y2 - y1)^2)
AB = sqrt((-4 - 4)^2 + (2 - 6)^2) = sqrt((-8)^2 + (-4)^2) = sqrt(64 + 16) = sqrt(80)
2. Length of side BC:
BC = sqrt((0 - (-4))^2 + (2 - 2)^2) = sqrt(4^2 + 0^2) = sqrt(16) = 4
3. Length of side AC:
AC = sqrt((0 - 4)^2 + (2 - 6)^2) = sqrt((-4)^2 + (-4)^2) = sqrt(16 + 16) = sqrt(32)
Now, let's compare the lengths of the sides:
AB = sqrt(80) ≈ 8.93
BC = 4
AC = sqrt(32) ≈ 5.66
Since all three sides have different lengths, triangle ABC is a scalene triangle.