Question

Directed segment AB goes from (23, 50) to (47, 209)

Point K is on AB.
The ratio of AK to KB is 2:10.
The x value of point K is

Answer 1

Kx = 27

Explanation:

A given line segment is divided in a given ratio by an unknown point. We want the x-coordinate of that point.

Setup

Point K on AB divides the segment so that ...

AK/KB = 2/10

5·AK = KB . . . . . multiply by 5

5(K -A) = B -K . . . . . resolve to separate points

5K +K = 5A +B . . . . add K+5A

Solution

K = (5A +B)/6 . . . . . divide by the coefficient of K

K = (5(23, 50) +(47, 209))/6 . . . . . fill in the given values

The coordinates of K are found by evaluating this expression.

K = ((5·23 +47)/6, (5·50 +209)/6) = (162, 459)/6

K = (27, 76.5)

The x-coordinate of point K is 27.