Final answer:
To find the coordinates of point B, take the averages of the x and y coordinates of points A and C. The length of AB can be found using the distance formula, and the length of BC can also be found using the distance formula.
Step-by-step explanation:
To find the coordinates of point B, we can use the formula for the midpoint of a line segment. The x-coordinate of the midpoint is the average of the x-coordinates of the endpoints, and the y-coordinate of the midpoint is the average of the y-coordinates of the endpoints. So, the x-coordinate of point B is (2+5)/2 = 3.5, and the y-coordinate of point B is (4+0)/2 = 2.
The length of AB can be found using the distance formula. Assuming the distance formula as sqrt((x2-x1)^2 + (y2-y1)^2), the length of AB is sqrt((3.5-2)^2 + (2-4)^2) = sqrt(1.5^2 + (-2)^2) = sqrt(2.25 + 4) = sqrt(6.25) = 2.5.
The length of BC can also be found using the distance formula. The coordinates of point B are (3.5,2) and the coordinates of point C are (5,0). So, the length of BC is sqrt((5-3.5)^2 + (0-2)^2) = sqrt(1.5^2 + (-2)^2) = sqrt(2.25 + 4) = sqrt(6.25) = 2.5.