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The line passing through (-4, -2) and (2, -3) is perpendicular to the line passing through (a, 5) and (2, -1). Find a.

Straight Line Eq

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Answer

By formula,

Slope = y2−y1x2−x1\dfrac{y2 - y1}{x2 - x1}

Let m1 be the slope of line passing through (-4, -2) and (2, -3), and m2 be the slope of line passing through (a, 5) and (2, -1).

Since, lines are perpendicular.

∴ m1.m2 = -1

⇒−3−(−2)2−(−4)×−1−52−a=−1⇒−3+22+4×−62−a=−1⇒−16×−62−a=−1⇒12−a=−1⇒−(2−a)=1⇒a−2=1⇒a=1+2=3.\Rightarrow \dfrac{-3 - (-2)}{2 - (-4)} \times \dfrac{-1 - 5}{2 - a} = -1 \\[1em] \Rightarrow \dfrac{-3 + 2}{2 + 4} \times \dfrac{-6}{2 - a} = -1 \\[1em] \Rightarrow \dfrac{-1}{6} \times \dfrac{-6}{2 - a} = -1 \\[1em] \Rightarrow \dfrac{1}{2 - a} = -1 \\[1em] \Rightarrow -(2 - a) = 1 \\[1em] \Rightarrow a - 2 = 1 \\[1em] \Rightarrow a = 1 + 2 = 3.

Hence, a = 3.

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