math question: shortest distance from point to a line? (Gr. 10)?

I believe you meant 3x + 5y - 4 = 0.

In that case, my answer is 5.32.

Try using the shortcut

d = [|A(x) + B(y) + C |] / √(A^2 + B^2 )

wherein x is the x-coordinate of the given point and y is the y-coordinate.

we want perpendicular line to x - 3y = 6 and includes element (0,0) x - 3y = 6 - 3y = - x + 6 y = a million/3x - 2 perpendicular slope is - 3 so the line is y = - 3x + b 0 = 0 + b 0 = b perpendicular line is y = - 3x Now we want the place those lines intersect y = - 3x y = a million/3 x- 2 - 3x = - a million/3x - 2 2 = 2 2/3 x 2 = 8/3x 6/8 = x 3/4 = x y = 3x so y = 3(3/4) = 9/4 ingredient of intersection is (3/4,9/4) now use distance formulation d = sqrt((x - x)^2 + (y - y)^2) in view that between the factors is (0,0) the equation turns into d = sqrt(x^2 + y^2) d = sqrt((3/4)^2 + (9/4)^2) d = sqrt(9/sixteen + 80 one/sixteen) d = sqrt(ninety/sixteen) d = sqrt(9)/sqrt(10)/4 d = 3sqrt(10)/4 d = 3/4(sqrt(10))