Th equation of a straight line that passes through point A(mid point (2,3) and (-8,15) )and point B (that lies 1/3 way from (-1,0) to (4,11) is given by ??
actually I am confused!!
calculated the mid-point of A = (-3,9) but now what how to proceed from now As B (lies 1/3 way from (-1,0) to (4,11)) i.e means another point I must it C .
Hints:
If point $\;P=(x,y)\;$ divides the segment of line with end points $\;A=(a_1,a_2)\;,\;\;B=(b_1,b_2)\;$ in the ratio $\;k:m\;$ , meaning:
$$\frac{|AP|}{|PA|}=\frac km$$
then the coordinates of $\;P\;$ are given by
$$\begin{cases}x=\frac{kb_1+ma_1}{k+m}\\{}\\y=\frac{kb_2+ma_2}{k+m}\end{cases}$$