Find the perimeter of △ABC with vertices A(−5, 5), B(3, −4), and C(−5, −4). Round your answer to the nearest hundredth.

Answer 1

length of two sides are 8 and 9. (8+9)x 2 = 17x2 = 34 = Perimeter

you know the 2 perpendicular sides are 8 and 9

from taking the difference of the y coordinates for the point with the same x coordinate

(-5, -5) and (-5,3) have the same x coordinate, so just subtract the y-coordinates 3 minus -5 = 8

look at (-5,3) and (4,3) They have the same y coordinates, so just subtract the x-coordinates, 4 minus -5 = 9

8 + 9 = half the perimeter = 17. Double it: Perimeter = 17x2 = 34

Answer 2

Alright, we can normally draw a right triangle with the line connecting our two points as the hypotenuse. What's the formula?

a² + b² = c²

Taking the square root of both sides...

c = √(a² + b²)

But how long are a and b? How far apart are our imaginary points??

c = √((x₂ - x₁)2 + (y₂ - y₁)²)

c = √((√-5 - 3)² + (5 - (-4))²) = √((-8)² + (9)²) = √(64 + 81) = √(145) = 12.04

There's the length of one side. Find the other two lengths and add them all up. Go!