Question

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

Answer 1

1.97 units

Explanation:

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

`d=(|ah+bk+c|)/(√(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=(|6(-2)+-1(3)+3|)/(√(6^2+(-1)^2) )`

`d=(|-12-3+3|)/(√(36+1) )`

`d=(12)/(√(37) )`

`d=1.97`