Question

The coordinates of the points P and Q are respectively (4, - 3) and (-1, 7) Then the abscissa of a point R on the line segment PQ such that $\frac{PR}{PQ}=\frac{3}{5}$ is

• A. $\frac{18}{5}$
• B. $\frac{17}{5}$
• C. $\frac{17}{8}$
• D. 1

Answer 1

Answer: (D)

1

Using the section formula, if a point $(x,y)$ divides the line joining the
points $(x_1,y_1)$ and $(x_2,y_2)$ internally
in the ratio $m:n$, then $(x,y)=(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n})$
Substituting $(x_1,y_1)=(4,-3)$ and $(x_2,y_2)=(-1,7)$ and $m=3,n=2$ in the section formula, we get
the abscissa of the point $\left(\frac{3(-1)+2\left(4\right)}{3+2}\right)=1$