For the line segment whose endpoints are X (1, 2) and Y (6, 7), find the x coordinate for the point located 1 over 3 the distance from X to Y.

Question

asked Jan 10, 2022 231k views

1 Answer

Kevin Dias · Answer 1 · 2022-01-14T14:53:15+0000

Answer:

P = ((8)/(3),(11)/(3))

Explanation:

Given

X = (1,2)

Y = (6,7)

Required

The point at 1/3 of XY

If the point is at 1/3 for X, then the other end (to Y) is 2/3

So, we have:

m:n = 1/3:2/3

Multiply by 3

m:n = 1:2

The point (P) is calculated using:

P = ((mx_2 + nx_1)/(m+n),(my_2 + ny_1)/(m+n))

This gives:

P = ((1*6 + 2*1)/(1+2),(1*7 + 2*2)/(1+2))

P = ((8)/(3),(11)/(3))