Question

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

Answer 1

Answer:

  2√5

Step-by-step explanation:

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

  $\text{distance}\,=\dfrac{|ax+by+c|}{\sqrt{a^2+b^2}}$

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

  2x +y -6 = 0

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

  $\text{distance}\,=\dfrac{|2\cdot 4+8-6|}{\sqrt{2^2+2^2}}=\dfrac{10}{\sqrt{5}}=2\sqrt{5}$

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