Shortest Distance

Geometry Level 1

What is the distance between point P P and line L L in the diagram?

4 4 4 3 4\sqrt{3} 8 8 Not enough information

Christopher Boo by Christopher Boo , 24, Singapore

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4 solutions

Kabir Malik
Mar 13, 2018

Drop a perpendicular from P to L. It forms a 30-60-90 triangle with hypotenuse 8. Using the 30-60-90 triangle identities, 8/2 = 4.

1 Helpful 1 Interesting 1 Brilliant 0 Confused
Padu Merloti
Oct 24, 2017

sin30=opp/8

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Frz Arkam
Jun 21, 2016

Shortest distance to line L from point P is a straight line. Since it will form a right triangle using trig we can show length of the line segment is 4

2 Helpful 0 Interesting 0 Brilliant 0 Confused

I have a small issue with the question: The position of your letter L is misleading. To achieve your answer, one needs to draw the line from P perpendicular to line L, to get the line of 8 as hypotenuse. But your letter L is lower thus creating a bit of confusion. It's just my opinion though.

Abdul Malik Richards - 4 years, 11 months ago

\sin 30^\circ = \frac{LP}{8}

\frac{1}{2} = \frac{LP}{8}

LP = 4

Abdul Malik Richards - 4 years, 11 months ago

Log in to reply

Why Latex not working? I followed the formatting guide. I'm sorry

Abdul Malik Richards - 4 years, 11 months ago

>clicks 4

>correct answer

>incorrect

TrisT . - 3 years, 4 months ago
Joseph Vera
Jun 18, 2018

SOH CAH TOA

sin(theta) = opposite/hypotenuse

sin(30) = 0.5 = (distance from P to L)/8

distance from P to L = 0.5 * 8 = 4

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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