To find the value of the fraction start fraction upper A upper D over upper A upper B end fraction, we need to determine the lengths of line segments AD and AB.
From the graph, we can see that line segment AD starts at point (0,0) and ends at point (9,0). Therefore, the length of AD is 9 units.
Line segment AB starts at point (3,0) and ends at point (4,5). To find the length of AB, we can use the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Using the coordinates, we can calculate the length of AB as follows:
Length AB = √((4 - 3)^2 + (5 - 0)^2)
= √(1^2 + 5^2)
= √(1 + 25)
= √26
Therefore, start fraction upper A upper D over upper A upper B end fraction is equal to 9 / √26.
To simplify the fraction, we need to rationalize the denominator by multiplying both the numerator and denominator by √26:
start fraction upper A upper D over upper A upper B end fraction = 9 / √26 * √26 / √26
= 9√26 / 26
So, the simplified value of start fraction upper A upper D over upper A upper B end fraction is 9√26 / 26.
None of the given options match this value.