Question

Find the coordinates of the points which divide the line segment joining a(-6,8) and b(8,-6) into four equal parts

Answer 1

Section formula :

Any point let say (x,y) divides the line joining points (x1 ,y1 ) & (x2 ,y2 ) in the ratio m:n, then co-ordinates were given by the formula

$x \: = \frac{x1 \times n \: + y1 \times m}{m + n}$

$y \: = \frac{y1 \times n \: + y2 \times m}{m + n}$

Given points A(−6,8) and B(8,−6)

(i) Point P(x,y) divides AB in the ratio 1:3

$x \: = \frac{( - 6) \times 3 + 8 \times 1}{1 + 3} = \frac{ - 5}{2}$

$y \: = \frac{8 \times 1 + ( - 6) \times 1}{1 + 3} = \frac{9}{2}$

Then,

(ii) Point Q(x,y) divides AB in the ratio 2:2=1:1

$x \: = \frac{( - 6) \times 1 + 8 \times 1}{1 + 1} = 1$

$y \: = \frac{8 \times 1 + ( - 6) \times 1}{1 + 1} = 1$

Then, Q(1,1)

(iii) Point R(x,y) divides AB in the ratio ratio 3:1

$x \: = \frac{( - 6) \times 1 + 8 \times 3}{1 + 3} = \frac{9}{2}$

$y \: = \frac{( 8) \times 1 + ( - 6) \times 3 }{1 + 3} = \frac{ - 5}{2}$