Question

Find the coordinates of the points which divide the line segment joining A(-2, 2) and B(2, 8) into four equal parts.

• A. , (0,5) ,
• B. (-1,7), (0,5) , (1, 13)
• C. , (0,5) ,
• D. , (0,5) ,

Answer 1

The correct option is A

, (0,5) ,

Let P,Q and R be the points which divides the line segment into four equal parts. P divides the line segment AB internally in the ratio of 1:3

Coordinates of point P($x_1,y_1$)

$x_1=\frac{1.(+2)+3(-2)}{3+1}=\frac{-6+2}{4}=-1$

$y_1=\frac{1.\left(8\right)+3\left(2\right)}{3+1}=\frac{14}{4}=\frac{7}{2}$

$p(x_1,y_1)=(-1,\frac{7}{2})$

Q divides the line segment in the ratio of 2:2 or 1:1

Q is the midpoint of line segment AB

Q$(x_2,y_2)$

Q $(\frac{-2+2}{2},\frac{2+8}{2})$= Q(0, 5)

Coordinates of Q are(0, 5)

R divides the line segment AB internally in the ratio of 3:1

R$(x_3,y_3)$

x₃ = = 1

$y_3=\frac{3\left(8\right)+1\left(2\right)}{1+3}=\frac{26}{4}=\frac{13}{2}$

Coordinates of R$(x_3,y_3)$ = $(1,\frac{13}{2})$

Coordinates of P,Q,R are $(-1,\frac{7}{2})$, (0,5) , $(1,\frac{13}{2})$ respectively.