Question

the segment joining (-8,1) and (11,7) is divided into four equal parts. Find the points of division nearest to ends.

Answer 1

Midpoint of line is:

$\begin{gathered} (\frac{x_1+x_2}{2}_{},\frac{y_1+y_2}{2}) \\ (\frac{-8+11}{2},\frac{7+1}{2}) \\ (\frac{3}{2},4) \end{gathered}$

Distance between two point.

x distance between F and G :

$\begin{gathered} X=11-(-8) \\ =19 \end{gathered}$

Y distance is:

$\begin{gathered} Y=7-1 \\ =6 \end{gathered}$

For 4 equal part is x and y distance is:

$\begin{gathered} x\text{ distance=}\frac{19}{4}=4.75 \\ y\text{ distance=}\frac{6}{4}=1.5 \end{gathered}$

so x and y coordinates is:

$\begin{gathered} (-8+4.75,1+1.5)_{} \\ (-3.25,2.5) \end{gathered}$

second coordinates is:

$\begin{gathered} (-3.25+4.75,2.5+1.5) \\ (1.5,4) \end{gathered}$

Then theird coordinates is:

$\begin{gathered} (1.5+4.75,4+1.5) \\ (6.25,5.5) \end{gathered}$

Fourth coordinates is:

$\begin{gathered} (6.25+4.75,5.5+1.5) \\ (11,7) \end{gathered}$