Geometry Fundamentals: Slope 4

Geometry Level 1

Straight line A of infinite length contains the points ( − 4 , 3 ) (-4,3) and ( 2 , 1 ) . (2,1).

Straight line B of infinite length contains the points ( 2 , 1 ) (2,1) and ( 11 , − 2 ) . (11,-2).

Are A and B the same line?

Yes No

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1 solution

Brilliant Mathematics Staff
Aug 1, 2020

The slope of line A is 1 − 3 2 − − 4 = − 2 6 = − 1 3 . \frac{1 - 3}{2 - -4} = \frac{-2}{6} =- \frac{1}{3}.

The slope of line B is − 2 − 1 11 − 2 = − 3 9 = − 1 3 . \frac{-2-1}{11-2} = \frac{-3}{9} = -\frac{1}{3}.

Both lines have the same slope and both lines travel through the point ( 2 , 1 ) (2,1) so A and B are the same line.

3 Helpful 0 Interesting 1 Brilliant 1 Confused

Potential mistake: It's important to remember that both points pass from the same point ( 2 , 1 ) (2,1) . Having the same slope is not enough to determine that they are the same line

Mahdi Raza - 10 months, 1 week ago

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Thanks. I've updated the problem statement to reflect this.

Brilliant Mathematics Staff - 10 months, 1 week ago

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