A point R lies on the line segment from \(A(-4,\,6)\) to \(B(8,\,-3)\) such that \(AR:RB=1:2\). What are the coordinates of R?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \((0,\,3)\)
The point dividing the segment from \((x_1,\,y_1)\) to \((x_2,\,y_2)\) internally in the ratio \(m:n\) is \(\displaystyle \left(\frac{mx_2+nx_1}{m+n},\,\frac{my_2+ny_1}{m+n}\right)\).
Here \(m=1\), \(n=2\), \(A(-4,\,6)\), \(B(8,\,-3)\)
x-coordinate: \(\displaystyle \frac{1\times8+2\times(-4)}{1+2}=\frac{8-8}{3}=0\)
y-coordinate: \(\displaystyle \frac{1\times(-3)+2\times6}{1+2}=\frac{-3+12}{3}=3\)
So \(R=(0,\,3)\)
