Triangle DEF has vertices located at D (2, 1), E (3, 5), and F (6, 2). Part A: Find the length of each side of the triangle. Show your work. (4 points)

Part B: Find the slope of each side of the triangle. Show your work. (3 points)

Part C: Classify the triangle. Explain your reasoning. (3 points)

Step-by-step explanation:

D(2, 1) E(3, 5) F(6, 2)

Part A

use the distance formula d= √(x2-x1)² +(y2-y1)²

DE = √(2-3)²+(1-5)² = √1 +16 = √17

EF= √(3-6)² +(5-2)² = √9 +9 = √18= √2*3*3= 3√2

DF = √(2-6)² +(1-2)² = √16 + 1= √17

Part B

slope is m= (y1-y1) / (x2-x1)

m of DE = (1-5) / (2-3) = -4/-1 = 4

m of EF =  (5-2) / (3-6)= 3/-3 = -1

m of DF =  (1-2) / (2-6) = -1/-4 = 1/4

Part C

the triangle has sides DE = DF = √17 and DE⊥DF because their slopes are negative reciprocals ( 4 and -1/4) so the triangle is an isosceles right triangle