Question

Find the points which divide the line segment joining A(-4, 0) and B(0, 6) into four equal parts.

Answer 1

Let P, Q and R are the points on the line segment joining the line AB.

Here AP = PQ = QR = RB

If AP = 1, PQ = 1, QR = 1 and RB = 1

Section formula

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

P divides the line segment in the ratio 1:3.

l = 1, m = 3, A(-4, 0) and B(0, 6).
Coordinates of P:

= $\frac{1\left(0\right)+3(-4)}{1+3}$, $\frac{1\left(6\right)+3\left(0\right)}{1+3}$

= $\frac{0-12}{4}$, $\frac{6+0}{4}$

= $\frac{-12}{4}$, $\frac{6}{4}$

P = (-3 , 3/2)

Q divides the line segment in the ratio 2 : 2.
So, Q is the mid-point of AB.

l = 1, m = 1
Coordinates of Q:

= $\frac{0-4}{2}$, $\frac{6+0}{2}$

= $\frac{-4}{2}$, $\frac{6}{2}$

Q = (-2 , 3)

R divides the line segment in the ratio 3:1.

l = 3, m = 1
Coordinates of R:

= $\frac{3\left(0\right)+1(-4)}{3+1}$, $\frac{3\left(6\right)+1\left(0\right)}{3+1}$

= $\frac{0-4}{4}$, $\frac{18+0}{4}$


= $\frac{-4}{4}$, $\frac{18}{4}$
R = (-1 , 9/2)

Hence the points divides the line segment into four parts are P (-3, 3/2), Q(-2, 3) and R(-1, 9/2).