Question

Find the equation of the
straight line passing through
(1, 2) and perpendicular to the
line x + y + 7 = 0.​

Answer 1

Given :-

• Point = (1, 2)
• Line = x + y + 7 = 0

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To find :-

• Equation of the straight line that is perpendicular to the given line.

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Solution :-

• As we have a point and equation of a line.

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❏ Let a point B(x,y) ⠀[Shown in figure]

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Let us write the given equation of the line in the form of y = mx + c.

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→ y = - x - 7

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• On comparing the both the equation, we get

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★ Slope of the line (m) = -1

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Now, we know that ...

Product of slope of two perpendicular lines is -1.

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According to the question

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→ Slope of AB × m = -1

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$\tt\longrightarrow{\bigg( \dfrac{y - 2}{x - 1} \bigg) \times -1 = -1}$

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$\tt\longrightarrow{\bigg( \dfrac{y - 2}{x - 1} \bigg) = \dfrac{-1}{-1}}$

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$\tt\longrightarrow{\bigg( \dfrac{y - 2}{x - 1} \bigg) = 1}$

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$\tt\longrightarrow{(y - 2) = 1(x - 1)}$

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$\tt\longrightarrow{y - 2 = x - 1}$

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$\bf\longrightarrow{x - y + 1 = 0}$

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Hence, the required equation of the line is x - y + 1 = 0.