Find the coordinates of the point which divides the line segment joining the points (4,−1) and (−2,−3) in the ratio 2 : 3 internally.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\left(\frac{8}{5},\frac{-9}{5}\right)\)
By the section formula, the point dividing the segment from \((x_1,y_1)\) to \((x_2,y_2)\) internally in the ratio \(m:n\) is \(\left(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n}\right)\). Here \(m=2\), \(n=3\), \((x_1,y_1)=(4,-1)\) and \((x_2,y_2)=(-2,-3)\).
As the division is internal, the point lies between the two given points, nearer to \((4,-1)\), the end of the smaller part of the ratio.
The first coordinate, \(x\): \(\displaystyle x=\frac{2(-2)+3(4)}{5}=\frac{8}{5}\)
The second coordinate, \(y\): \(\displaystyle y=\frac{2(-3)+3(-1)}{5}=\frac{-9}{5}\)