Answer:
Kx = 27
Step-by-step explanation:
A given line segment is divided in a given ratio by an unknown point. We want the x-coordinate of that point.
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
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.
