Question

Find the distance of origin from the line 15x - 8y = - 56

Answer 1

To find the distance from the origin \((0, 0)\) to the line given by the equation \(15x - 8y = -56\), we can use the formula for the distance \(d\) from a point \((x_0, y_0)\) to a line given by the equation \(Ax + By + C = 0\):

\[
d = \frac{|Ax_0 + By_0 + C|}{\sqrt{A^2 + B^2}}
\]

First, we need to rewrite the line equation \(15x - 8y = -56\) in the standard form \(Ax + By + C = 0\):

\[
15x - 8y + 56 = 0
\]

Here, \(A = 15\), \(B = -8\), and \(C = 56\).

Next, substitute the coordinates of the origin \((x_0, y_0) = (0, 0)\) into the formula:

\[
d = \frac{|15(0) + (-8)(0) + 56|}{\sqrt{15^2 + (-8)^2}} = \frac{|56|}{\sqrt{225 + 64}}
\]

Calculate the denominator:

\[
\sqrt{225 + 64} = \sqrt{289} = 17
\]

Now substitute this back into the distance formula:

\[
d = \frac{56}{17}
\]

Thus, the distance from the origin to the line \(15x - 8y = -56\) is

\[
\frac{56}{17}
\]

This can be approximated as \(3.29\) if a decimal representation is needed.

So, the final answer is:

\[
\frac{56}{17}
\]