Question

Find the distance between line LK y=-x+1 and line DE y=-x+13

Answer 1

`d=6√(2)`

Explanation:

To find the distance between two parallel lines, use this formula:

`d=\fracc_(2)-c_(1) {\sqrt{1+m^(2) } }`

With each line being in this form: y = mx + c1 and y = mx + c2

In line LK, m = -1 and c1 = 1

In line DE, m = -1 and c2 = 13

Now we input this into the formula:

`d =\frac13-1{\sqrt{1+(-1)^(2) } }`

We simplify even more:

`d =(12)/(√(2) ) \\`

Usually the square root does not belong on the bottom, so multiply the whole fraction by
`(√(2) )/(√(2) )`. *When a square root is squared, what is left is the radicand*

`d=(12√(2) )/(2 )\\`

12/2 is equal to 6, so

`d=6√(2)`