Correct Answer - Option 1 :
\(-2\over3\)
Concept:
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.
- Slope of the perpendicular line have their product = -1
Equation of a line passing through (x1, y1) and (x2, y2) is:
\(\rm {y-y_1\over x-x_1}={y_2-y_1\over x_2-x_1}\)
Calculation:
The line passing through the points (3, 2) and (1, -1)
The equation of the line is
\(\rm {y-2\over x-3}={-1-2\over1-3}\)
3x - 2y - 5 = 0
y = \(3\over2\)x - \(5\over2\)
⇒ Slope(m1) = \(3\over2\) and c1 = \(-5\over2\)
Now for the slope of the perpendicular line (m2)
m1 × m2 = -1
⇒ \(3\over2\) × m2 = -1
⇒ m2 = \(-2\over3\)