christian7533
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What is the distance from point (– 1, 3) to the line 3x – 4y = 10?​

Sagot :

Answer:

5 units

Step-by-step explanation:

The distance from a point (m, n ) to the line Ax + By + C = 0 is given by

d = [tex]\frac{|Am+Bn+C|}{\sqrt{A^2+B^2} }[/tex]

For the point (- 1, 3 ) , with m = - 1 and n = 3

3x - 4y = 10 ( subtract 10 from both sides )

3x - 4y - 10 = 0

with A = 3 , B = - 4 , C = - 10

d = [tex]\frac{|3(-1)+(-4)3-10|}{\sqrt{3^2+(-4)^2} }[/tex]

   = [tex]\frac{|-3-12-10|}{9+16}[/tex]

   = [tex]\frac{|-25|}{\sqrt{25} }[/tex]

    = [tex]\frac{25}{5}[/tex]

     = 5

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