The straight line 3x + 4y = 24 cuts the y - axis at the point A and cuts the
x - axis at the point. What is the distance AB?​

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)