Find the coordinates of P so that P partitions the segment AB in the ratio 1:7 if A(7,14) and B(−1,−2).

Answer 1

Could the point (0,0) also work? If direction on the segment is mandatory then not. Something to think about.

Answer 2

There are a total of 8 segments (since 1+7 = 8). So, P is 1/8 of the way from A to B.

As we move along AB from A to B, x decreases by 8 and y decreases by 16.

x-coordinate of P = (x-coordinate of A) + (1/8)(change in x from A to B) = 7 + (1/8)(-8) = 6

y-coordinate of P = (y-coordinate of P + (1/8)(change in y from A to B) = 14 + (1/8)(-16) = 12

So, P = (6, 12)