Question

What is the distance between (4,8), 6=y+ 2x

Answer 1

2√5

Explanation:

The formula for the distance between a point (x, y) and a line in general form, ax +by +c = 0 is ...

`\text{distance}\,=(|ax+by+c|)/(√(a^2+b^2))`

The general form of your equation for the line is ...

2x +y -6 = 0

so the distance to point (x, y) = (4, 8) is ...

`\text{distance}\,=(|2\cdot 4+8-6|)/(√(2^2+2^2))=(10)/(√(5))=2√(5)`

The distance between the point and line is 2√5.