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Question: The distance of the point (–2, 3) from the line \(x - y = 5\) is...

The distance of the point (–2, 3) from the line x−y=5x - y = 5 is

A

525 \sqrt { 2 }

B

252 \sqrt { 5 }

C

353 \sqrt { 5 }

D

535 \sqrt { 3 }

Answer

525 \sqrt { 2 }

Explanation

Solution

p=∣x1−y1−512+12∣=∣−2−3−512+12∣=∣−102∣=52p = \left| \frac { x _ { 1 } - y _ { 1 } - 5 } { \sqrt { 1 ^ { 2 } + 1 ^ { 2 } } } \right| = \left| \frac { - 2 - 3 - 5 } { \sqrt { 1 ^ { 2 } + 1 ^ { 2 } } } \right| = \left| \frac { - 10 } { \sqrt { 2 } } \right| = 5 \sqrt { 2 }