Desperate! Help!

Question

Molly is putting a triangular sandbox in her backyard. She draws the plan for the sandbox on a coordinate plane. Vertex A is at (−4,6)(−4,6), Vertex B is at (6,1)(6,1), and Vertex C is at (0,−9)(0,−9). Calculate the lengths of the sides and put them in order from shortest to longest.

1. Side BC
2. Side AB
3. Side AC

Answer 1

BC is from (6,1) to (0,-9) a^2 = 36+100, a =sqr136 = 2sqr34

AB is from (6,1) to (-4,6) c^2 = 100+25, c =sqr125 = 5sqr5

AC is from (-4,6) to (0,-9) b^2 = 16+225 b=sqr241

use the distance formula, which is a version of the Pythagorean theorem

longest side of a right triangle is the square root of the sum of squares of the other two sides

d^2 = x^2 +y^2 where d= the distance between the 2 points, x = the difference in x coordinates of the 2 points and y = the difference in the y coordinates of the 2 points

AB<BC<AC

shortest is AB

longest is AC