The distance from the line x=4 to the given point (-2,5) is 6 units .
Distance formula from line to point :
The distance from the line ax+by+c=0 to the point (u,v) is given by the formula
[tex]distance=\frac{|au+bv+c|}{\sqrt{a^{2} +b^{2} } }[/tex]
In the given question
the equation of the line is [tex]x=4[/tex]
taking all the terms to Left side we get
[tex]x-4=0[/tex]
[tex]1.x+0.y-4=0[/tex]
given the points (-2,5)
From above values we the values as a=1 , b=0 , c=-4 , u=-2 , v=5 .
Substituting the values in the distance formula we get
[tex]d=\frac{|1*(-2)+0*(5)-4|}{\sqrt{1^{2} +0^{2} } }[/tex]
[tex]=\frac{|-2+0-4|}{1} \\ \\ =|-6|\\ \\ =6[/tex]
Therefore , the distance from the line x=4 to the given point (-2,5) is 6 units.
Learn more about Distance Formula here https://brainly.com/question/14348586
#SPJ4
