heeeeeeeeeeeelp

Question

a triangle ABC has a right angle at B. the vertices are A(-2,9), B(2,8) and C(1,z). the value of z is:

Answer 1

z=4

there are two possible right triangles, but you want the one with angle B=90 degrees

that's C(1, 4)

it helps to plot the points on at least a rough graph

A(-2,9), B(2,8) C(1,z)=(1,4)

set the slopes of AB and CB = negative inverses

slope of AB = difference in y coordinates divided by difference in x coordinates = "rise over run"

=(9-8)/(-2-2) = -1/4

slope of BC = (8-z)/(2-1) = (8-z)/1= 8-z

let 8-z = negative inverse of -1/4 = 4

8-z =4

z =8-4=4

z=4

C = (1,4)

slope of BC = (4-8)/(1-2) = -4/-1 = 4

slope of A B= -1/4

AB is perpendicular to BC, creating a right triangle, if AB's slope = the negative inverse of BC's slope