Q. 104.1( 84 Votes )
Find the equation of the line passing through (–3, 5) and perpendicular to the line through the points (2, 5) and (–3, 6).
Given points are (2, 5) and (-3, 6).
We know that slope, m =
We know that two non-vertical lines are perpendicular to each other if and only if their slopes are negative reciprocals of each other.
We know that the point (x, y) lies on the line with slope m through the fixed point (x0, y0), if and only if, its coordinates satisfy the equation y – y0 = m (x – x0)
∴ y – 5 = 5(x – (-3))
⇒ y – 5 = 5x + 15
⇒ 5x + 15 – y + 5 = 0
⇒ 5x – y + 20 = 0
Ans. The equation of the line is 5x – y + 20 = 0.
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