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)

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:

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

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

1 is your x-coordinate

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

7/2 is your y-coordinate.

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