Find the equation of the line perpendicular to the line x − 7y + 5 = 0 and passing through the point (2, −3).
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Slope of x − 7y + 5 = 0: y = x/7 + 5/7 ⇒ m = 1/7. Perpendicular slope m' = −7. Line through (2, −3): y + 3 = −7(x − 2) ⇒ y = −7x + 11. 7x + y − 11 = 0.
📅 Year 2023
Q1
CBSE Board Exam 20233 Marks
The perpendicular from the origin to a line meets it at (−2, 9). Find the equation of the line.
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The perpendicular from origin meets at (−2, 9), so slope of perpendicular = 9/−2 = −9/2. Slope of the line = 2/9 (negative reciprocal). Line through (−2, 9) with slope 2/9: y − 9 = (2/9)(x + 2) ⇒ 9y − 81 = 2x + 4. 2x − 9y + 85 = 0.