Question

Find the coordinates of P that partitions segment AB , where A (2,3) and B (14,9), so that AP:PB is a 1:2 ratio. Also, find the coordinate of a point M that bisects segment AB​

Answer 1

For Point P, you need to recognize that a 1:2 ratio means that AP will be 1/3 of AB and PB will be 2/3 of AB.

So you need to find the change in the x-values, 14-2 = 12, and then add 1/3 of that change to the x-value of A.

Then you need to find the change in the y-values, 9-3 = 6, and then add 1/3 of that change to the y-value of A.

For the bisector, that's another way to say you'll split AB into two even pieces.  For this, it's the same as what we just did, but you need to find 1/2 of the two respective changes (1/2 of the x-change and 1/2 the y-change).