Slopes of Parallel and Perpendicular Lines (GMAT/GRE/CAT/Bank PO/SSC CGL) | Don't Memorise

TL;DR

The slopes of parallel lines are equal, while the slopes of perpendicular lines have a product of -1.

Transcript

How are the slopes of two parallel lines related? Take these two parallel lines for example. If the slope of this line is M1 and that of this one is M2, then how are M1 and M2 related? You don't really have to think here. It's obvious. The tilt or the inclination is the same. M1 will be equal to M2. The slopes of parallel lines are the same. Okay, ... Read More

Key Insights

• 🫥 Slopes of parallel lines are equal, while slopes of perpendicular lines have a product of -1.
• 🏙️ To find the equation of a perpendicular bisector, find the slope using the coordinates of one line and the midpoint to determine the y-intercept.
• 😥 Plotting and connecting points are important steps in determining the equation of a perpendicular bisector.
• ❣️ The coordinates of the midpoint of a line segment can easily be found by averaging the x and y coordinates of the endpoints.

Questions & Answers

Q: How are the slopes of parallel lines related?

The slopes of parallel lines are equal. If one line has a slope of M1 and another has a slope of M2, then M1 = M2.

Q: How are the slopes of perpendicular lines related?

The slopes of perpendicular lines are negative reciprocals of each other. If one line has a slope of M3 and another has a slope of M4, then M3 * M4 = -1.

Q: How can we find the equation of a perpendicular bisector?

To find the equation of a perpendicular bisector, first find the slope using the coordinates of one line, and then find the midpoint of that line to determine the y-intercept. Substitute the values into the slope-intercept form (y = mx + b).

Q: What is the equation of the perpendicular bisector in the given example?

The equation of the perpendicular bisector CD, with a slope of 1/2, is y = x/2. The coordinates of the midpoint, 2 comma 1, were used to find the y-intercept (b = 0).

Summary & Key Takeaways

• Parallel lines have the same slope, while perpendicular lines have slopes that are negative reciprocals of each other.

• To find the equation of a perpendicular bisector, first, plot the given points and connect them. Then find the slope using the coordinates of one of the lines, and find the midpoint of the line to determine the y-intercept.

• For the example given, the slope of CD (perpendicular bisector) is 1/2, and the equation is y = x/2.