Question
Download Solution PDFFind the equation of the line perpendicular to the line x - 3y + 5 = 0 and passes through the point (2, -4).
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
The general equation of a line is y = mx + c
Where m is the slope and c is any constant
- The slope of parallel lines is equal.
- The slope of the perpendicular line have their product = -1
Equation of a line with slope m and passing through (x1, y1)
(y - y1) = m (x - x1)
Calculation:
Given line x - 3y + 5 = 0
⇒ y =
⇒ Slope(m1) =
Now for the slope of the perpendicular line (m2)
m1 × m2 = -1
⇒
⇒ m2 = -3
Perpendicular line has the slope -3 and passes through (2, -4)
∴ Equation of the perpendicular line is
(y - y1) = m (x - x1)
⇒ y - (-4) = -3 (x - 2)
⇒ y + 3x - 2 = 0
Last updated on Jun 30, 2025
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