Find the coordinates of the point which divides the line segment joining the points (4, -3) and (8, 5) in the ratio 3 : 1 internally?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (7, 3)
By the section formula, the point dividing the join of \((x_1,y_1)\) and \((x_2,y_2)\) internally in the ratio \(m:n\) is \(\displaystyle\left(\frac{mx_2+nx_1}{m+n},\ \frac{my_2+ny_1}{m+n}\right)\). The point is 3 parts from the first point and 1 part from the second, so it lies nearer \((8,5)\).
\(m=3\), \(n=1\); \((x_1,y_1)=(4,-3)\), \((x_2,y_2)=(8,5)\)
\(\displaystyle x=\frac{3\times8+1\times4}{3+1}=\frac{28}{4}=7\)
\(\displaystyle y=\frac{3\times5+1\times(-3)}{3+1}=\frac{12}{4}=3\)
Shortcut: A point dividing a segment internally lies between its two ends.
x must lie between 4 and 8, and y between −3 and 5
Only (7, 3) satisfies both, so it is the answer without any working