Which of the following points is collinear with (0,0) and (2,1)?
A) (-2,-1)
B) (-1,-2)
C) (-1,2)
D) (1,-2)
E) (1,2)

It’s pretty quick just to draw these all and see, but it’s even faster to recognize that when a line goes through (0, 0), then all of its other points will tell you the slope all by themselves. This is because slope, generally speaking, is change in y divided by change in x, calculated thusly:


When one of the points is (0, 0), that simplifies:


So really here all you’re looking for is another set of points with the same \dfrac{y}{x} ratio as (2, 1) has. (–2, –1) works perfectly.

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