Question

Find the distance between the pair of parallel lines with the given equations.y = -5xy = -5x + 26O A) 5 unitsO B) 14.14 unitsC) C) 5.10 unitsO D) 6 units

Answer 1

Consider two lines with the following equations:

`y_1=mx+c`

and

`y_2=mx+c_2`

the distance d between these two parallel lines is given by the following equation:

First, we need to take one of the lines and convert it to standard form. For example, take the line:

y = -5x + 26

then, we obtain:

-5x-y+26=0

in this case, we get that

A = -5

B= -1

C = 26

Now we can substitute A, B, and C into our distance equation along with a point, (x1,y1) from the other line. We can pick any point on the line y2. Just plug in a number for x, and solve for y. I will use x = 2, to obtain:

y = -5(2) = -10

then

(x1,y1) = (2,-10)

Replacing these values into the distance equation, we obtain:

`d\text{ = }\frac-5(2)+(-1)(-10)+26{\sqrt[]{(-5)^2+(-1)^2}}`

that is:

`d\text{ = }\frac{\sqrt[]{(-5)^2+(-1)^2}}=\frac{26}{\sqrt[]{26}}=5.09\approx5.10`

so that, the correct answer is:

`5.10\text{ units}`