A triangle has vertices at A(6,5), B(−3, 2), C(−1, −4).
Find the slope of each side.
Is the triangle a right triangle?
Explain why or why not.
To find the slope of a side, we can use the formula:
m = (y2 - y1)/(x2 - x1)
Let's find the slopes of each side:
1) Slope of side AB:
mAB = (2 - 5)/(-3 - 6) = -3/-9 = 1/3
2) Slope of side BC:
mBC = (-4 - 2)/(-1 - (-3)) = -6/2 = -3
3) Slope of side AC:
mAC = (-4 - 5)/(-1 - 6) = -9/-7 ≈ 1.286
Now, let's determine if the triangle is a right triangle. One way to do this is by checking if two sides of the triangle are perpendicular. Two lines are perpendicular if and only if the product of their slopes is -1.
Checking the slopes:
mAB * mBC = (1/3) * (-3) = -1
Since the product of the slopes of sides AB and BC is -1, we can conclude that these sides are perpendicular. Therefore, the triangle is a right triangle.