Question

A point M on a segment with endpoints (-2, 1) and ( 6, 7) partitions the segment in a 3:5 ratio. Find M. Show all of your work.

Answer 1

Solution

We are given the endpoints P(-2, 1) and Q(6, 7)

and we are also given the segment ratio to be 3:5

We want to find the coordinate of M

Solution

Sum of ratio = 3 + 5 = 8

The next thing we will do is to subtract the coordinate

That is Q - P

$\begin{gathered} Q-P=(6,7)-(-2,1) \\ Q-P=(6-(-2),7-1)_{} \\ Q-P=(6+2,6) \\ Q-P=(8,6) \end{gathered}$

We will start from P and therefore use the ratio between P and M

The ratio between them P and M is 3

Therefore, we have

$\begin{gathered} \frac{3}{8}\times(Q-P)=\frac{3}{8}\times(8,6) \\ \frac{3}{8}\times(Q-P)=(3,\frac{9}{4}) \end{gathered}$

We are left with getting the Point M

$\begin{gathered} M=P+(3,\frac{9}{4}) \\ M=(-2,1)+(3,\frac{9}{4}) \\ M=(-2+3,1+\frac{9}{4}) \\ M=(1,\frac{13}{4}) \end{gathered}$

Therefore, The point M is

$(1,\frac{13}{4})$