Answer:
[tex]\sqrt{37}[/tex]
Step-by-step explanation:
The distance d between a point (m , n ) and a line in the form
Ax + By + C = 0 , is calculated as
d = [tex]\frac{|Am+Bn+C|}{\sqrt{A^2+B^2} }[/tex]
Here (m, n ) = (6, 2 ) and
6x - y = - 3 ( add 3 to both sides )
6x - y + 3 = 0 → A = 6, B = - 1, C = 3
d = [tex]\frac{|6(6)+-1(2)+3|}{\sqrt{6^2+(-1)^2} }[/tex]
= [tex]\frac{|36-2+3|}{\sqrt{36+1} }[/tex]
= [tex]\frac{|37|}{\sqrt{37} }[/tex]
= [tex]\frac{37}{\sqrt{37} }[/tex] × [tex]\frac{\sqrt{37} }{\sqrt{37} }[/tex]
= [tex]\frac{37\sqrt{37} }{37}[/tex] ← cancel 37 on numerator/ denominator
= [tex]\sqrt{37}[/tex]
