Question

6. Find the point that partitions segment AB

in a 2:1 ratio.
10
y₁
9
8
7
6
5
4
32
-
A
illustrative
B
Mathematics
1 2 3 4 5 6 7 8 9 10

Answer 1

(5, 6 1/3)

Explanation:

You want the point that partitions AB in a 2:1 ratio.

Solution

Let that point be P. Then the required ratio is ...

AP/PB = 2/1

AP = 2·PB . . . . . . multiply by PB

P -A = 2(B -P) . . . . write as the difference of coordinates

3P = 2B +A . . . . . . . solve for P

Substituting the given coordinates, we have ...

3P = 2(7, 8) +(1, 3) = (14 +1, 16 +3)

P = (15, 19)/3 = (5, 6 1/3)

The point that partitions AB into the ratio 2:1 is (5, 6 1/3).