Line segment AB has endpoints A(−5,−8) and B(2,6). What are the coordinates of the point that partitions AB according to the part-to-part ratio 4:3?

Answer 1

add 4 to -5 to get -1

-8 +8 = 0

the point is (-1,-0)

4:3 means you want 4/(4+3) = 4/7 of the way from A to B

You want 4/7 of the difference of the x coordinates. (4/7)(2--5) = (4/7)7 = 4. Add that to -5, the x coordinate of point A to get 4-5=-1

do the same with the y coordinates: (4/7)(6--8) = (4/7)14 = 8. Add 8 to -8 = 0

the point is (-1,0)

the line through theses points has slope 2, as x increases by 1, y increases by 2

the difference in A and B x coordinates is 7, the difference in y coordinates is 14 (twice 7)

you want 4/7 of the differences or 4/7 times 7 = 4 and 4/7 times 14 or 8

from (-5,-8) add 4 to -5 and add 8 to -8 to get (-1,0) the x intercept of the line