Coordinate Geometry – Master Slope and Get Points!
When my classes arrive at the math session that covers coordinate geometry, there is a general outbreak of panic:
“I haven’t done this since high school…”
“Which one is the y-axis again?”
“Seriously, I’m going to grad school for history – why do I need to know this?!”
What people don’t realize is that coordinate geometry only requires you to memorize a few things, and they’re almost all related to the concept of slope. A line’s slope just measures its slant – the larger the slope’s absolute value, the closer it is to a vertical line.
Any time the slope is expressed as a fraction, remember the expression “rise over run” – the slope represents the ratio of the vertical rate of change (in the numerator) to the horizontal rate of change (in the denominator). For example: A line with a slope of 1/3 moves up 1 unit, for every 3 units that it moves to the right.
Let’s see how one piece of very key knowledge can help us – check out the following Quantitative Comparison:
We’re asked to compare the lengths of a right triangle’s legs. Since the lengths are perpendicular and start at the origin, we can use what we know about slope to determine the relationship between them.
We know that the line’s slope is -9/10 (if that didn’t jump out at you, review slope-intercept form – it’s the other important thing to know for coordinate geometry questions). What does this tell us? It means that for every 9 units the line goes down, it goes 10 units to the right.
Well, we can use this to compare AB and BC. Since they cross at a right angle, they represent the vertical and horizontal change of the line – AB is 9 units, to BC’s 10 units. And we’re done – Quantity B is greater.
Remember: Any topic with which a lot of test-takers struggle, is high-yield on the GRE. So the more comfortable you are applying the definition of slope, the sooner you’ll fly by the competition!