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} ((x_1+x_2)/(2)_{},(y_1+y_2)/(2)) \\ ((-8+11)/(2),(7+1)/(2)) \\ ((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=}(19)/(4)=4.75 \\ y\text{ distance=}(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}`