The line 3x+4y=24 cuts the x-axis at point a and the y-axis at b. find the coordinate of a and b the length of ab point c is on the line such that c is equidistant from x and y-axis. find coordinate of c.

If line 3x + 4y = 24 cuts the x axis at point A, then point A is ur x intercept of line 3x + 4y = 24. To find the x int, sub in 0 for y and solve for x.
3x + 4y = 24
3x + 4(0) = 24
3x = 24
x = 24/3
x = 8so point A is (8,0) <===

if line 3x + 4y = 24 cuts the y axis at point B, the point B is the y int. of 3x + 4y = 24. To find the y int, sub in 0 for x and solve for y
3x + 4y = 24
3(0) + 4y = 24
4y = 24
y = 24/4
y = 6so point B is  (0,6) <===

if point C is equidistant from point A and point B, then it is the midpoint.
midpoint formula : (x1 + x2) / 2, (y1 + y2) / 2
(8,0)x1 = 8 and y1 = 0
(0,6)...x2 = 0 and y2 = 6
time to sub and solve
m = (8 + 0)/2 , (0 + 6)/2
m = (8/2),(6/2)
m = (4,3) <=== this is point C