Find the distance from point A(0,5) to y=-3x-5

Answer 1

Find the distance from point A(0,5) to y=-3x-5

Another method:

First, find the equation for the line perpendicular to the given line, and passing through the given point:

y = mx + b

To be perpendicular,the slope (m) will be 1/3. Since x = 0 at the given point, b = 5

So we have

y = x/3 + 5

Now, solve the pair of equations to find the intersection.

Finally, find the distance from the intersection to the given point. (square root of thesum of the squares of x and y displacements)

Answer 2

d = (5+5)/sqrt(10) = 3.162

The formula is d = (Ax₀ + By_o+C)/sqrt(A² + B²)

Where the equation of the line is Ax + By + C = 0 and the point is (x₀,y_o).

You can find good derivations of this formula on line.