Question

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)

Answer 1

So, you could solve this without the drawing, but I thought it might be easier to explain with a model.
Basically, you can find the right triangles that connect each of the dots, then use the pythagorean theorem to calculate the long sides of each of those triangles (the hypotenuse). That will give you the distance between the dots.
I'll draw out what I mean, using points D and E as an example

Answer 2

See how when we draw a right triangle with the line connecting DE as the hypotenuse, we find a triangle with a height of 4 and a width of 1.
Now, we can calculate the hypotenuse of this triangle with the Pythagorean theorem.
\[a ^{2}+b ^{2}=c ^{2}\]
Replacing the variables with the values we have gives us
\[4^{2}+1^{2}=c ^{2}\]
which simplifies to 16+1=c^2 or 17=c^2.
Remember that c is the length of the hypotenuse, but we have c-squared. So, we take the square root of both sides to find that c=\[\sqrt{17}\]
You could use a calculator to find that that is about 4.12, or maybe your instructor will allow just \[\sqrt{17}\]

Answer 3

Anyway, that's the distance between D and E. See if you can use that method to find the distance between E and F, then D and F.

Answer 4

Here's a drawing to (hopefully) point you in the right direction