SATHEE: Straight Line and Pair of Straight Lines 1 Question 64

Straight Line and Pair of Straight Lines 1 Question 64

64. Two equal sides of an isosceles triangle are given by the equations $7 x - y + 3 = 0$ and $x + y - 3 = 0$ and its third side passes through the point $(1, - 10)$ . Determine the equation of the third side.

$(1984, 4 M)$

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Solution:

The equation of any line passing through $(1, - 10)$ is $y + 10 = m (x - 1)$ .

Since, it makes equal angles, say $θ$ , with the given lines, therefore

$\tan θ = \frac{m - 7}{1 + 7 m} = \frac{m - (- 1)}{1 + m (- 1)} \Rightarrow m = \frac{1}{3} or - 3$

Hence, the equations of third side are

$\begin{aligned} y + 10 = \frac{1}{3} (x - 1) or y + 10 = - 3 (x - 1) \\ i.e. x - 3 y - 31 = 0 or 3 x + y + 7 = 0 \end{aligned}$

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Straight Line and Pair of Straight Lines 1 Question 64

64. Two equal sides of an isosceles triangle are given by the equations 7x−y+3=0 and x+y−3=0 and its third side passes through the point (1,−10). Determine the equation of the third side.

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64. Two equal sides of an isosceles triangle are given by the equations $7 x - y + 3 = 0$ and $x + y - 3 = 0$ and its third side passes through the point $(1, - 10)$ . Determine the equation of the third side.