Question

A point Q on a segment with endpoints A(2,-1) and C(4,2) partitions the segment in a 3:1 ratio. Find Q.

Answer 1

Since we want a 3 to 1 ratio, we need 4 parts total.

Answer 2

Consider the x and y parts separately.
First the x: From 2 to 4 is 2 units. If you divide 2 units into 4 equal parts, each part is 1/2

Answer 3

3 of those equal parts is 3/2 or 1 1/2
If you add 1 1/2 to the starting point 2 you get 2+1 1/2=3 1/2
So the x coordinate of the desired point Q is 3 1/2

Answer 4

Now you try the same thing and see if you can find the y coordinate.

Answer 5

so would I add 1/.75 to -1?

Answer 6

@Mertsj

Answer 7

From -1 to 2 is 3 units. If you divide that by 4 each of the equal parts is 3/4
Three of those equal parts is 3 times 3/4 which is 9/4 which is 2 1/4
Add the 2 1/4 to -1 and you end up at 1 1/4
That is the y coordinate of the point Q

Answer 8

Ohhh thank you for helping me!(:

Answer 9

yw