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

easy question but as long as its easy

Answer 2

Answer:

The coordinates of the points P, Q  and R are P(2,3), Q(3,4) and R(4,5).

Step-by-step explanation:

It is given that P, Q, R and S divide the line segment joining the points A(1, 2)

and B(6, 7) in 5 equal parts.

Section formula,

$(x,y)=(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})$

P divides the line AB in 1:4.

$P(x,y)=(\frac{1(6)+4(1)}{1+4},\frac{1(7)+4(2)}{1+4})=(2,3)$

Q divides the line AB in 2:3.

$Q(x,y)=(\frac{2(6)+3(1)}{2+3},\frac{2(7)+3(2)}{2+3})=(3,4)$

R divides the line AB in 3:2.

$R(x,y)=(\frac{3(6)+2(1)}{3+2},\frac{3(7)+2(2)}{3+2})=(4,5)$

Therefore the coordinates of the points P, Q  and R are P(2,3), Q(3,4) and R(4,5).