Question

What kind of triangle is shown?
Answer

scalene

equilateral

isosceles

right

Answer 1

First order of business, we need to figure out the lengths of the triangle:

the side going from (-2,2) to (-6,7) will be called side A.

The length of side A can be determined using the distance formula:
\[\Delta x ^2 + \Delta y^2 = Side(A) ^2\]

[(-6) - (-2)]^2 + [7 - 2]^2 = (Side A)^2

(-4)^2 + (5)^2 = (side A)^2

16 + 25 = A^2

41 = A^2
\[A = \sqrt{41}\]

Now lets call the side going from (-2,2) to (-2,8) side B:

Using the same equation, we will end up getting

0 + 36 = B^2

B = 6

Now lets call the last side going from (-6,7) to (-2,8) side C. Using the distance formula, we get:

16 + 1 = C^2
\[C = \sqrt{17}\]

Now since all the sides are different lengths, the triangle must be a Scalene Triangle.

Answer 2

oh ok i get it now :) thank you