Question

GRE Review: Coordinate Geometry

Answer 1

\({\bf{Basics:}}\)


> if a point is on the x-axis the y-coordinate is 0
> if a point is on the y-axis the x-coordinate is 0

sometimes you will be given a point like this:



we don't know what the x-value is (we do know that it's positive) but we know that it's on the x-axis so we can assign a variable to be x

(a,0) where a is positive

Answer 2

\({\bf{Calculating~Distance~Btwn~Points:}}\)

> if the two points are on the same horizontal line, subtract the x-coordinates
> if the two points are on the same vertical line, subtract the y-coordinates
this will work even if you aren't given numbers, but rather variables

if neither of these conditions apply you can use the distance formula, or, if you forget, construct a right triangle where the distance between the two points is the hypotenuse, then use the pythagorean theorem to calculate the hypotenuse length

Answer 3

\({\bf{Slopes:}}\)
> horizontal line has 0 slope; vertical line has undefined slope
> upward slanting lines have + slope, downward slanting lines have - slope



> parallel lines have the same slope
> perpendicular lines have opposite-reciprocal slope
ex: if slope of a line is 1/2, then the slope of a perpendicular line has slope -2

flip the numerator and denominator, then multiply by -1

> slope formula:



always double check the sign of the slope after you have calculated it

Answer 4

Anyway, that's the end of my tutorial, I hope it was a helpful resource. Source material is the 19th edition Barron's prep book for the new GRE.