Answer:
3x - 4y = -10
-4y = -3x - 10
y = (3/4)x + (5/2)
The slope of the perpendicular line will be -4/3.
From (3, -4), go up 4 units, then left 3 units. You will be at (0, 0), so the equation of this line is y = (-4/3)x.
(3/4)x + (5/2) = (-4/3)x
9x + 30 = -16x
25x = -30
x = -6/5, so y = (-4/3)(-6/5) = 24/15 = 8/5
d = √((3 - (-6/5))² + (-4 - (8/5))²)
= √((21/5)² + (-28/5)²)
= (1/5)√(21² + (-28)²)
= (1/5)√(441 + 784)
= (1/5)√1,225
= (1/5)(35)
= 7