Question

what are the coordinates of point R ?a line segment has endpoints s(-9. -4) t(6, 5). point R lies on ST such that the ratio of SR to RT is 2:1

Answer 1

Find the difference between the coords first: x: 6-(-9)=15, y: 5-(-4)=9.

Now add the numbers of the ratio together: 2+1=3 and divide the distances by this : 5 and 3 respectively.

SR is 2/3 along the x distance so that’s ⅔ of 15=10 and 2/3 along the y distance which is ⅔ of 9 which is 6.

So we add 10 to the x-coord of the S to get 10-9=1; and 9 to the y-coord to get 6-4=2.

This gives us R(1,2).