Question

Which is the distance between the point with the coordinates (-2,3) and the line with the equation 6x-y=-3

Answer 1

Answer:

1.97 units

Step-by-step explanation:

The distance from a point (h,k) to a line $ax+by+c=0$ is given by:

$d=\frac{|ah+bk+c|}{\sqrt{a^2+b^2} }$

The given line is $6x-y=-3$. or $6x-y+3=0$.

This implies that: a=6, b=-1 and c=3

The given point is (-2,3)

This implies that: h=-2 and k=3

We substitute into the formula to get:

$d=\frac{|6(-2)+-1(3)+3|}{\sqrt{6^2+(-1)^2} }$

$d=\frac{|-12-3+3|}{\sqrt{36+1} }$

$d=\frac{12}{\sqrt{37} }$

$d=1.97$