Question

Points $P,Q,R$ and $S$ divide the line segment joining the points $A(1,2)$ and $B(6,7)$ in $5$ equal parts. Find the coordinates of the points $P,Q$ and $R$.

Answer 1

P, Q, R, S divide the line segment AB on the ratio $1:4,2:3,3:2,4:1$ respectively.

From above P divides AB in $1:4$ ratio

coordinates of P using section formula,

$\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n}$

here $m=1$ and $n=4,x_1=1,x_2=6,y_1=2,y_2=7$

$\Rightarrow$$\frac{6+4}{5},\frac{7+8}{5}$

$\Rightarrow$$(2,3)=$ coordinates of P

Similarly,

Coordinates of Q,

Q divide AB in $2:3$ ratio,

$\Rightarrow$ $\frac{12+3}{5},\frac{14+6}{5}$

$\Rightarrow$ $(3,4)=$ coordinates of Q

Similarly,

R divide AB in $3:2$ ratio,

Coordinates of R,

$\Rightarrow$ $\frac{18+2}{5},\frac{21+4}{5}$

$\Rightarrow$ $(4,5)=$ coordinates of R