Question

Triangle ABC has vertices located at A( 0, 2), B (2, 5), and C (−1, 7).

Part A: Find the length of each side of the triangle. Show your work.

Part B: Find the slope of each side of the triangle. Show your work.

Part C: Classify the triangle. Explain your reasoning.

Answer 1

Part A) use the distance formula to find the length of AB, BC, and CA.

Part B) use the slope formula to find the slopes of AB, BC, and CA.

Part C) look at the side lengths. If they’re all equal then the triangle is equilateral. If only two sides are equal it’s isosceles. If all three sides are different it’s scalene. Also look at the slopes: if any two slopes are opposite reciprocals, those two slopes make a right angle and thus it’s a right triangle. If not, try plotting the triangle, looking at the angles, and classify as acute or obtuse.

I’ll attach a diagram to help illustrate:

Answer 2

alright

Answer 3

@vocaloid how do i do part b to find all 3 together

Answer 4

for part B, do each side separately

for side AB you would calculate the slope between points A and B
for side BC you would calculate the slope between points B and C
for side CA you would calculate the slope between points C and A