Question

A point T on a segment with endpoints D (1, 4) and F (7, 1) partitions the segment in a 3:1 ratio. Find T. You must show all work to receive credit. (10 points)

Answer 1

If a line segment is partitioned having ending points (1,4),(7,1) in the ratio of 3:1 then the coordinates will be (25/4,7/4)

Given Ending points (1,4), (7,1) and the ratio 3:1 in which the line segment is divided.

If we are given the ratio m:n and the ending points of the line segment then the coordinates of the point dividing the segment will be (mx2+nx1/m+n,my2+ny1/m+n)

Putting the values of m=3 n=1 x1=1 y1=4 x2=7 and y2=1 we get

Coordinates (x,y)=(3*7+1*1/3+1,3*1+1*4/3+1)

=(21+1/4,3+4/4)

=(22/4,7/4)

Hence the point which is dividing the line segment having ending points (1,4) and (7,1) in the ratio 3:4 is (22/4,7/4).

Learn more about ratio here brainly.com/question/2328454

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