Question

If X and Y are points X(2, -1) and Y(-3,-2) respectively , What are the coordinates of P such that $XP=\frac{5}{7}XY?$

• A. $P(\frac{-11}{7},\frac{-12}{7})$
• B. $P(\frac{-12}{7},\frac{-11}{7})$
• C. $P(\frac{-1}{14},\frac{-17}{14})$
• D. $P(\frac{-17}{14},\frac{-1}{14})$

Answer 1

The correct option is A $P(\frac{-11}{7},\frac{-12}{7})$

Let the required point be $P(a,b)XP=\frac{5}{7}XY\frac{XP}{XY}=\frac{5}{7}Now,letXP=5kandXY=7kSo,YP=XY-XP=7k-5k=2k\frac{XP}{YP}=\frac{5k}{2k}=5:2\text{By section formula,}a=\frac{5(-3)+2\left(2\right)}{5+2}=\frac{-15+4}{7}=\frac{-11}{7}b=\frac{5(-2)+2(-1)}{5+2}=\frac{-10-2}{7}=\frac{-12}{7}\text{So, the coordinates of P are}(\frac{-11}{7},\frac{-12}{7})$.

Thus, option (a) is correct.