Let AB be the line segment such that R (h, k) divides it in the ratio 1: 2.
Let the coordinates of A and B are (0, y) and (x, 0) respectively.
We know that the coordinates of a point dividing the line segment joining the points (x1, y1) and (x2, y2) internally in the ratio m: n are .
∴ h = 2x/3 and k = y/3
⇒ x = 3h/2 and y = 3k
∴ A = (0, 3k) and B = (3h/2, 0)
We know that the equation of the line passing through the points (x1, y1) and (x2, y2) is given by
⇒ 3h(y - 3k) = -6kx
⇒ 3hy - 9hk = -6kx
⇒ 6kx + 3hy = 9hk
Dividing both the sides by 9hk, we get,
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