Coordinates in math

Question

What are the coordinates of the point on the directed line segment of (-3,-9) to (9,7) that partitions the segment into a ratio of 5 to 3

Answer 1

-3 to 9 = 12

divide 12 by 5+3= 8

12/8= 3/2

multiply 3/2 by 5 = 15/2

add 15/2 to -3 = 9/2= x coordinate

-9 to 7 = 16

divide 16 by 8 = 2

multiply 2 by 5 = 10

add 10 to -9 = 1 = y coordinate

the point is (9/2,1) or (4.5, 2)

it divides the line segment into a 5:3 ratio

it may help to plot the points and a line segment connecting them

divide the line segment in half, then in half again

then in half again, now it's cut in 8 parts each 1/8 of the full line segment

find the x and y coordinates of the 5/8 part of the full segment

midpoint of the line segment is (3,-1)

then midpoint from (3,-1) to to right end (9,7) is (6,3)

midpoint between (3,-1) and (6,3) is (4.5,2)

find each midpoint by finding the average x and y coordinates of the end points

midpoint of the entire line segment = (3,-1) = ((-3+9)/2, (-9+7)/2) = (6/2,-2/2)= (3,-1)

midpoint from (3,-1) to (9,7) = (6,3) = ((9+3)/2, (7-1)/2) = (12/2, 6/2)= (6,3)

midpoint from (3,-1) to (6,3) = ((3+6)/2, (-1+3)/2) = (9/2, 4/2) = (4.5,2)