Find the ratio in which the y-axis divides the line segment joining the points (-4, -6) and (10, 12). Also, find the coordinates of the point of division

Solution

Let the y-axis divide the line segment joining the points ( -4, -6 ) and ( 10, 12 )in the ratio k:1 and the point of the intersection be ( 0, y ).

Using section formula, we have

$[\frac{10 k + (- 4)}{k + 1} . \frac{12 k + (- 6)}{k + 1}] = 0, y ∴ \frac{10 k - 4}{k + 1} = 0 \Rightarrow 10 k - 4 = 0 \Rightarrow k = \frac{4}{10} = \frac{2}{5} Thus the y - axis divides the line segment joining the given points in the ratio 2 : 5 ∴ y = \frac{12 k + (- 6)}{k + 1} = \frac{12 x \frac{2}{5} - 6}{\frac{2}{5} + 1} = \frac{(\frac{24 - 30}{5})}{(\frac{2 + 5}{5})} = - \frac{6}{7} Thus, the coordinates of the point of division are (0, - \frac{6}{7})$

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Coordinate Geometry

Find the ratio in which the y-axis divides the line segment joining the points (-4, -6) and (10, 12). Also, find the coordinates of the point of division

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Prove that the diagonals of a rectangle ABCD, with vertices A(2, -1), B(5, -1), C(5, 6) and D(2, 6), are equal and bisect each other.

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