Question

A point M on a segment with endpoints (-1, 1) and ( 7, 7) partitions the segment in a 3:5 ratio. Find M. You must show all work to receive credit . (

Answer 1

The coordinates of point M after the partition is (2, 3.25).

What are coordinates and how to determine coordinates?

• A coordinate system in geometry is a system that uses one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.

We have:

• Endpoints = (-1,1) and (7,7)
• Ratio, m : n = 3 : 5

The coordinates of point M is then calculated using:

$M=\frac{1}{m+n} *(mx_{2}+nx_{1} , my_{2} +ny_{1} )$

So, we have:

$M=\frac{1}{3+5} * (3*7+5*-1,3*7+5*1)$

Evaluate the sum and the product:

$M=\frac{1}{8} *(16,26)$

Evaluate the product:

$M=(2,3.25)$

The coordinates of point M is (2, 3.25)

Therefore, the coordinates of point M after the partition is (2, 3.25).

Know more about coordinates here:

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