Math help Big ideas

Question

Find the coordinates of point $P$ along the directed line segment AB, from A (-2,-4) to B (6,1) so that the ratio of AP to PB is 3 to 2

Answer 1

For the x coordinate.

What is the distance from -2 to 6?

Divide that distance by 5 and give 3 of that to the -2

For the y coordinate:

What is the distance from -4 to 1?

Divide that distance by 5 and give 3 of that to the -4

What is the new ordered pair?

Any questions>

Answer 2

Since the ratio of AP to PB is 3 to 2, we are dividing line segment AB into 5 equal sections where P is 3/5 of the way from A to B as we travel along line segment AB.

As we move along AB from A to B, the x-coordinate increases by 8 and the y-coordinate increases by 5.

x-coordinate of P = -2 + (3/5)(8) = -2 + 24/5 = 14/5

y-coordinate of P = -4 + (3/5)(5) = -4 + 3 = -1

P = (14/5, -1)