SOLUTION: I need help on this please 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. P

Algebra ->  Triangles -> SOLUTION: I need help on this please 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. P      Log On


   

Question 1177582: I need help on this please

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.
Part B: Find the slope of each side of the triangle. Show your work.
Part C: Classify the triangle. Explain your reasoning.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

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.
the length of each side is equal to the distance between endpoints
the length of the side DE is equal to the distance between (2, 1) and (3, 5)
Solved by pluggable solver: Distance Between 2 points
The distance formula is sqrt%28%28%28x%5B2%5D-x%5B1%5D%29%5E2%29%2B%28%28y%5B2%5D-y%5B1%5D%29%5E2%29%29. Plug in the numbers,
sqrt%28%28%283-%282%29%29%5E2%29%2B%28%285-%281%29%29%5E2%29%29
sqrt%281%5E2%2B4%5E2%29 The distance is 4.12310562561766.



so, DE=4.12 (approximately)

the length of the side DF is equal to the distance between (2, 1) and (6, 2)
Solved by pluggable solver: Distance Between 2 points
The distance formula is sqrt%28%28%28x%5B2%5D-x%5B1%5D%29%5E2%29%2B%28%28y%5B2%5D-y%5B1%5D%29%5E2%29%29. Plug in the numbers,
sqrt%28%28%286-%282%29%29%5E2%29%2B%28%282-%281%29%29%5E2%29%29
sqrt%284%5E2%2B1%5E2%29 The distance is 4.12310562561766.



so, DF=4.12 (approximately)
the length of the side EF is equal to the distance between ((3, 5) and (6, 2)
Solved by pluggable solver: Distance Between 2 points
The distance formula is sqrt%28%28%28x%5B2%5D-x%5B1%5D%29%5E2%29%2B%28%28y%5B2%5D-y%5B1%5D%29%5E2%29%29. Plug in the numbers,
sqrt%28%28%286-%283%29%29%5E2%29%2B%28%282-%285%29%29%5E2%29%29
sqrt%283%5E2%2B-3%5E2%29 The distance is 4.24264068711928.



EF=+4.24(approximately)


Part B:
Find the slope of each side of the triangle. Show your work.
DE passes through (2, 1) and (3, 5)
slope is
Solved by pluggable solver: Finding the slope


Slope of the line through the points (2, 1) and (3, 5)



m+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+x%5B1%5D%29


m+=+%285+-+1%29%2F%283+-+2%29


m+=+%284%29%2F%281%29


m+=+4



Answer: Slope is m+=+4



DF passes through (2, 1) and (6, 2)
slope is
Solved by pluggable solver: Finding the slope


Slope of the line through the points (2, 1) and (6, 2)



m+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+x%5B1%5D%29


m+=+%282+-+1%29%2F%286+-+2%29


m+=+%281%29%2F%284%29


Answer: Slope is m+=+1%2F4



side EF passes through ((3, 5) and (6, 2)
slope is
Solved by pluggable solver: Finding the slope


Slope of the line through the points (6, 2) and (3, 5)



m+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+x%5B1%5D%29


m+=+%285+-+2%29%2F%283+-+6%29


m+=+%283%29%2F%28-3%29


m+=+-1



Answer: Slope is m+=+-1





Part C:
Classify the triangle. Explain your reasoning.

Triangle DEF is an isosceles triangle because sides DE and DF are the same length.