Answer:
C = (5, 4)
Explanation:
You want the coordinates of point C, located 3/4 of the way from A(-4, -2) to B(8, 6).
Dividing point
That point is ...
C = A +3/4(B -A)
C = (-4, -2) + (3/4)((8, 6) -(-4, -2))
C = (-4, -2) + (3/4)(8+4, 6+2) = (-4, -2) + (3/4)(12, 8) = (-4, -2) +(9, 6)
C = (-4 +9, -2 +6)
C = (5, 4)
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Additional comment
Equivalently,
C = (3B +A)/4 = (3(8, 6) +(-4, -2))/4 = (24 -4, 18 -2)/4 = (5, 4)
The method shown above may be more intuitive. The formula shown here is a result of simplifying the one used above.
When computing the weighted average of the coordinates, the nearest point (B) gets the higher weight (3/4).