Answer:
P = (3, 3 2/7)
Step-by-step explanation:
The desired point P is the weighted average of the end point values. The weights are the numbers in the ratio of segment lengths. The smallest weight is used for the end point closest to the largest division.
P = (5N +2M)/(5+2) = (5(7, 7) +2(-7, -6))/7 = (35-14, 35-12)/7
. P = (21, 23)/7
P = (3, 3 2/7)
_____
The x-distance from M to N is 7-(-7) = 14 units. The x-distance from P to M must be 5/(5+2) = 5/7 of that, so is (5/7)14 = 10 units. So, the x-coordinate of P is ...
Mx +10 = Px
-7 +10 = 3 . . . . x-coordinate of P
The corresponding y-coordinate can be found from a graph or by a similar calculation.
My +5/7(Ny -My) = Py
Py = -6 +(5/7)(7-(-6)) = -6 +65/7 = -6 +9 2/7 = 3 2/7 . . . . y-coordinate of P
