find the distance from the point (6,4) to the line y=x+4

Answer 1

y=x+4 is a 45 degree line with y-intercept at (0,4)

the horizontal distance to the point (6,4) from (0,4) is 6. That's the base of a right isoscelese triangle with height = base also = 6. The hypotenuse = sqr(36+36) = 6sqr2

draw a line perpendicular from the line to the point (6,4). That's the distance from the line to that point.

that line also creates another right isoscelese triangle, but with hypotenuse = 6 and sides = 6/sqr2

that's the distance from the point (4,6) to the line y=x+4: 6/sqr2 = 3sqr2 = about 4.242

It definitely helps if you just draw a rough sketch on a standard x y graph