Question

Given the points A(-1,2) and B(7,8), find the coordinates of the point P on directed line segment AB that partitions AB in the ratio 1:3
A. (1, 7/2)B. (3,5)C.(5, 13/2)D. (7,8)

Answer 1

Now despite what you may believe, 1:3 is not 1/3 in this situation. In this case, it means "1 equal part to 3 equal parts", which is a total of 4 equal parts. In short, this question is to place point P 1/4 the distance from A to B.

Firstly, how far apart is -1 from 7 (the x-coordinates)? That would be 8 units. Multiply 1/4 by 8:

$\frac{1}{4}\times \frac{8}{1}=\frac{8}{4}=2$

Next, how far apart is 2 from 8 (the y-coordinates)? That would be 6 units. Multiply 1/4 by 6:

$\frac{1}{4}\times \frac{6}{1}=\frac{6}{4}=\frac{3}{2}$

Next, since from -1 to 7 you are increasing, add 2 to -1:

$-1+2=1$

1 is your x-coordinate

Next, since from 2 to 8 you are increasing, add 3/2 to 2:

$\frac{2}{1}\times \frac{2}{2}=\frac{4}{2}\\\\\frac{4}{2}+\frac{3}{2}=\frac{7}{2}$

7/2 is your y-coordinate.

Putting it together, your answer is A. (1, 7/2)