Exams › SSC CGL (Prelims) › General

Are the lines \(3x-4y=12\) and \(4x+3y=7\) perpendicular?

1. Yes
2. No
3. Only if they intersect at the y-axis
4. Cannot be determined

Correct answer: Yes

Solution

For \(3x-4y=12\), slope \(m_1=\frac{3}{4}\). For \(4x+3y=7\), slope \(m_2=-\frac{4}{3}\). Since \(m_1m_2=\frac{3}{4}\cdot\left(-\frac{4}{3}\right)=-1\), the lines are perpendicular.

Related SSC CGL (Prelims) General questions

• What is the equation of a line passing through \((0,4)\) with slope \(-2\)?
• What is the slope of the line perpendicular to $y = 5x - 8$?
• Which line has slope \(-2\) and passes through \((3,5)\)?
• A line \(L\) is the perpendicular bisector of the line segment joining points \(P(4,6)\) and \(Q(10,2)\). What is the y-intercept of line \(L\)?
• Find the slope of the line $4x - 5y = 10$.
• Find the equation of the perpendicular bisector of the line segment joining the points $(1,5)$ and $(5,9)$.

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