Find the distance from (-6,-1) to the line defined by y=3x+7. Express as a radical or a number rounded to the nearest hundredth.
+130511 There is a "formula" for finding the distance from a point to a line written in the form Ax + By + C = 0......it is given by:
d = l Am + Bn + C l / √(A2 + B2) where (m,n) is the given point
So....the given line can be written as 3x - 1y + 7 = 0 .....and we have
d = l 3(-6) - 1(-1) + 7 l / √((3)2 + (-1)2) = l -18 + 1 + 7 l / √10 = l -10 l / √10 =
10 / √10 = √10 units
(BTW...if you're interested to see how this "formula" was derived, look here.......http://www.intmath.com/plane-analytic-geometry/perpendicular-distance-point-line.php )
+130511 There is a "formula" for finding the distance from a point to a line written in the form Ax + By + C = 0......it is given by:
d = l Am + Bn + C l / √(A2 + B2) where (m,n) is the given point
So....the given line can be written as 3x - 1y + 7 = 0 .....and we have
d = l 3(-6) - 1(-1) + 7 l / √((3)2 + (-1)2) = l -18 + 1 + 7 l / √10 = l -10 l / √10 =
10 / √10 = √10 units
(BTW...if you're interested to see how this "formula" was derived, look here.......http://www.intmath.com/plane-analytic-geometry/perpendicular-distance-point-line.php )
