The distance between both lines is 2.24 units
Step-by-step explanation:
There is no straight method to find the distance between two lines. The distance can be found out by finding a point on one line and then finding the distance of that point from the other line. The y-coordinate of point is obtained by putting any value of x in equation . The x and y combined give us the point.
Given
[tex]y=2x\\Putting\ x=1\\y=2(1)\\y=2\\So, the\ point\ on\ y=2x\ is\ (1,2)[/tex]
We have to find the distance of this point from y=2x+5
[tex]y=2x+5\\Subtracting\ y\ from\ both\ sides\\y-y=2x+5-y\\2x-y+5=0[/tex]
The formula for finding distance of a point (x,y) from a line is:
[tex]d=\frac{|Ax+By+C|}{\sqrt{A^2+B^2}}[/tex]
A=2
B=-1
C=5
Putting the values in the formula
[tex]d=\frac{|(2)(1)+(-1)(2)+5|}{\sqrt{(2)^2+(-1)^2}}\\d=\frac{|2-2+5|}{\sqrt{4+1}}\\d=\frac{|5|}{\sqrt{5}}\\d=\frac{5}{\sqrt{5}}\\d=2.236\ units[/tex]
Rounding off will give: 2.24 units
The distance between both lines is 2.24 units
Keywords: Equations of lines
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