Question

Find the distance between the point (7,6) and the line y=2x-1

Answer 1

The distance between a line with the equation ax + by + c = 0 and a point (A, B) is given by the formula:

`\fracaA+bB+c{\sqrt[]{a^2+b^2}}`

So, before we can apply this formula, let's rewrite the equation of the line in the form ax + by + c = 0:

y = 2x - 1

2x - 1 = y

2x - 1 - y = y - y

2x - y - 1 = 0

So, in this case, we have:

a = 2

b = -1

c = -1

Also, since we want to find the distance between this line and the point (7, 6), we have:

A = 7

B = 6

Using those in the formula, we find the distance:

`\frac{\sqrt[]{a^2+b^2}}=\frac{\sqrt[]{2^2+(-1)^2^{}}}=\frac{\sqrt[]{4+1}}=\frac7{\sqrt[]{5}}=\frac{7}{\sqrt[]{5}}`

Therefore, that distance is

`\frac{7}{\sqrt[]{5}}`