Question

For the directed line segment whose endpoints are B(0, 0) and C(12, 24), find the point whose coordinates are 3/4 from B to C.

Answer 1

(9, 18)

Explanation:

If point P is 3/4 of the distance from B to C, it means that ...

BP/BC = 3/4

(P - B) = 3/4(C - B) . . . . . . multiply by BC = (C-B)

P = B + 3/4C -3/4B . . . . . add B

P = (1/4)B +(3/4)C = (B +3C)/4

P = ((0, 0) +3(12, 24))/4 = (36, 72)/4 = (9, 18)

The desired point is (9, 18).

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As we showed, since B = (0, 0), the point is 3/4 of the coordinates of C.