The point R divides the line segment AB, where A (-4,0) and B (0,6) are such that AR=3/4AB Find - Maths - Coordinate Geometry

Question

The point R divides the line segment AB, where A (-4,0) and B
(0,6) are such that AR=3/4AB Find the coordinates of R

Lalit Mehra · Accepted Answer

Given, R divides the line segment joining A( – 4, 0) and B(0, 6) such that $AR = \frac{3}{4} AB$ .

$AR = \frac{3}{4} AB$

$∴ AR = \frac{3}{4} (AR + RB)$

⇒ 4AR = 3AR + 3RB

⇒ AR = 3RB

$\Rightarrow \frac{AR}{RB} = \frac{3}{1}$

∴ R divides the line segment AB in the ration 3 : 1

Coordinates of the point dividing the line segment joining (x₁, y₁) and (x₂, y₂) in the ration m : n is $(\frac{m x_{2} + n x_{1}}{m + n}, \frac{m y_{2} + n y_{1}}{m + n})$

Coordinates of R

$= (\frac{3 \times 0 + 1 \times (- 4)}{3 + 1}, \frac{3 \times 6 + 1 \times 0}{3 + 1}) = (\frac{0 - 4}{4}, \frac{18 + 0}{4}) = (\frac{- 4}{4}, \frac{18}{4}) = (- 1, \frac{9}{2})$

Thus, the coordinates of R is $(- 1, \frac{9}{2})$ .

The point R divides the line segment AB, where A (-4,0) and B (0,6) are such that AR=3/4AB. Find the coordinates of R.