Question

Given in a plane the points A(-1,4),B(2,3),C(4,5),D(m,7)

Calculate m knowing that AB // CD

helppppp step by step

Answer 1

m = -2

Explanation:

slope of AB

(4-3)/(-1-2)= 1/-3 = -1/3

parallel lines have the same slope

slope of CD = -1/3

we can now find the line that passes through the point C

y-5= -1/3(x-4)

y = -1/3 x +4/3 +5

y = -1/3 x + (4+15)/3

y = -1/3 x + 19/3

this line must passes also through the point D

we know its y, so:

7 = -1/3 x + 19/3

(7 * 3) = (-1/3 x + 19/3) * 3

21 = - x + 19

x = 19 - 21

x = -2