9514 1404 393
Answer:
(c) (3, 3)
Step-by-step explanation:
Point E partitions both the x-distance and the y-distance in the ratio 2 : 1. That is, for either the x-coordinates or the y-coordinates, ...
CE : ED = 2 : 1
Try the answers with the x-coordinates.
CE : ED = (1 -(-1)) : (5 - 1) = 2 : 4 . . . . incorrect
CE : ED = (-3 -(-1)) : (5 -(-3)) = -2 : 8 . . . . incorrect
CE : ED = (3 -(-1)) : (5 -3) = 4 : 2 = 2 : 1 . . . . correct
CE : ED = (-1 -(-1)) : (5 -(-1)) = 0 : 6 . . . . incorrect
The only viable choice is (3, 3).
_____
Alternate solution
For a partitioning of m : n, the desired point is ...
E = (n×C +m×D)/(m+n)
For partitioning of 2 : 1, the desired point is ...
E = (1×(-1, -3) + 2×(5, 6))/(2+1) = (-1+10, -3 +12)/3
E = (3, 3)
