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प्रश्न
The line passing through (−4, −2) and (2, −3) is perpendicular to the line passing through (a, 5) and (2, −1). Find a.
उत्तर
Slope of the line passing through (−4, −2) and (2, −3) is m1
`m_1 = (-3 + 2)/(2 + 4) = (-1)/6`
Slope of the line passing through (a, 5) and (2, −1) is m2
`m_2 = (-1 - 5)/(2 - a) = (-6)/(2 - a)`
Since, the lines are perpendicular
`m_1 = (-1)/m_2`
∴ `(-1)/6 = (-1)/((-6)/(2 - a))`
∴ `(-1)/6 = (2 - a)/6`
∴ (2 – a) = –1
∴ a = 3
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