Question

3.(06.04 MC)A point Mon a segment with endpoints X(1, -2) and (10,3) partitions the segment in a 4:1 ratio. Find M. You must show all work

Answer 1

The formula used to calculate the coordinate of a line segment using ratio m:n is given below as

$(\frac{mx_2+nx_1}{m+n}),(\frac{my_2+ny_1}{m+n})_{}$

Where the given values are

$\begin{gathered} (1,-2)=(x_1=1,y_1=-2) \\ (10,3)=(x_2=10,y_2=3) \\ m=4,n=1 \end{gathered}$

By substituting the value, we will have

$\begin{gathered} (\frac{mx_2+nx_1}{m+n}),(\frac{my_2+ny_1}{m+n})_{} \\ \frac{(4\times10)+(1\times1)}{4+1},\frac{(4\times3)+(1\times-2)}{4+1} \end{gathered}$$\begin{gathered} \frac{(4\times10)+(1\times1)}{4+1},\frac{(4\times3)+(1\times-2)}{4+1} \\ =\frac{40+1}{5}\frac{,12-2}{5} \\ =(\frac{41}{5},\frac{10}{5}) \\ =(\frac{41}{5},2) \end{gathered}$

Hence,

The value of the coordinate of M is = ( 41/5, 2)