Question

Find the distance from point P to the given line

Answer 1

Answer:

The distance from point P, P(-2,4) to the given line y= 2x-2 is 1.56

Step-by-step explanation:

We need to find the distance from point P to the given line

P(-2,4) , y= 2x-2

The formula used is: $Distance=\frac{|Ax_1+By_1+C|}{\sqrt{A^2+B^2} }$

Where A, B and C are points of line i.e Ax+By+C=0

and x_1 and y_1 are points of P

So, y=2x-2 in Ax+By+C=0 is:

2x-y-2=0

A=2,

B=-1

C=1

Point given is P(-2,4)

x_1=-2

y_1=4

Putting values and finding distance

$Distance=\frac{|Ax_1+By_1+C|}{\sqrt{A^2+B^2} }\\Distance=\frac{|2(-2)+-1(4)+1|}{\sqrt{(-2)^2+(4)^2} }\\Distance=\frac{|-4-4+1|}{\sqrt{4+16} }\\Distance=\frac{|-7|}{\sqrt{20}}\\Distance=\frac{7}{\sqrt{20} }\\Distance=\frac{7}{4.5}\\Distance=1.56$

So,  the distance from point P, P(-2,4) to the given line y= 2x-2 is 1.56