Find the distance

Geometry Level 3

What is the perpendicular distance between the point A and straight line B?


The answer is 36.

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1 solution

We know the distance formula from a point (0,0) to a straight line is d = C A 2 + B 2 d=\frac { ∣C∣ }{ \sqrt { { A }^{ 2 }+{ B }^{ 2 } } } .
Here the equation of straight line y = m x + c y=mx+c . where m = 4 3 m=\frac { 4 }{ 3 } .
again from the slope we can tell, when the straight line moves 3' horizontally it moves 4' vertically. so when the line moves 30' horizontally it moves 40' vertically. so c becomes 40+20=60'.
therefore y = ( 4 / 3 ) x + 60 y=(4/3)x +60 or 4 x 3 y + 180 = 0 4x-3y+180=0 .
so the distance d = 180 4 2 + 3 2 = 180 5 = 36. d=\frac { 180 }{ \sqrt { { 4 }^{ 2 }+{ 3 }^{ 2 } } } = \frac {180 }{ 5 } = 36.
so, d=36'


Thanks.

I have updated the answer to 36.

FYI, to type Latex, you just need to add \ ( \ ) (no spaces) around your math code. I've edited it so that you can refer to it.

Calvin Lin Staff - 6 years, 7 months ago

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