Question

Find the point on the line 8x+7y-2=0 which is closest to the point (-6,-4).

Answer 1

y=(2/7)-(8/7)x

The point (-6,-4) should be located on a line perpendicular to the original equation

Thus use use the negative inverse of the slope m (which is -(8/7) and make it +(7/8))

Plug in (-6,-4) into the general line equation: y=mx+b
and solve for b

set the two equations equal to each other and you get the closest point.


To find the distance between use:
distance formula
d=sqrt((x2-x1)^2+(y2-y1)^2)

Answer 2

Remember, the shortest distance between a line and a point is a perpendicular line between the point and the other point on the line.