Moon:

GRE Review: Coordinate Geometry

2 months ago
Moon:

2 months ago
Moon:

$${\bf{Basics:}}$$ |dw:1542728450204:dw| > 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: |dw:1542728486211:dw| 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

2 months ago
Moon:

$${\bf{Calculating~Distance~Btwn~Points:}}$$ > 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 |dw:1542728675273:dw|

2 months ago
Moon:

$${\bf{Slopes:}}$$ > horizontal line has 0 slope; vertical line has undefined slope > upward slanting lines have + slope, downward slanting lines have - slope |dw:1542728769430:dw| > 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: |dw:1542728823328:dw| always double check the sign of the slope after you have calculated it

2 months ago
Moon:

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.

2 months ago