Question

Find the coordinates of the point which divides the line segment joining the points $A(4,-3)$ and $B(9,7)$ in the ratio $3:2$

• A. $P(-7,3)$
  
• B. $P(7,3)$
• C. $P(8,3)$
• D. $P(7,2)$

Answer 1

Answer: (B)

$P(7,3)$

Using the section formula, if a point $(x,y)$ divides the line joining the points $(x_1,y_1)$ and $(x_2,y_2)$ in the ratio $m:n$, then $(x,y)=(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n})$
Let the required point be $(x,y)$

Substituting $(x_1,y_1)=(4,-3)$ and $(x_2,y_2)=(9,7)$ and $m=3,n=2$ in the section formula, we get
$(x,y)=(\frac{3\left(9\right)+2\left(4\right)}{3+2},\frac{3\left(7\right)+2(-3)}{3+2})$
$(x,y)=(\frac{27+8}{5},\frac{21-6}{5})$
$(x,y)=(\frac{35}{5},\frac{15}{5})$
$(x,y)=(7,3)$