Four line segments are graphed on a coordinate plane. All four lines meet at point E.Line segment Upper A Upper E begins at left parenthesis 0 comma 0 right parenthesis and ends at left parenthesis 4 comma 5 right parenthesis. Line segment Upper B Upper E begins at left parenthesis 3 comma 0 right parenthesis and ends at left parenthesis 4 comma 5 right parenthesis. Line segment Upper C Upper E begins at left parenthesis 6 comma 0 right parenthesis and ends at left parenthesis 4 comma 5 right parenthesis. Line segment Upper D Upper E begins at left parenthesis 9 comma 0 right parenthesis and ends at left parenthesis 4 comma 5 right parenthesis.

Question

Question
Multiple Choice

Use the graph to answer the question.
What is start fraction upper A upper D over upper A upper B end fraction in simplest form?
(1 point)
Responses

start fraction 10 over 3 end fraction
Image with alt text: start fraction 10 over 3 end fraction

start fraction 1 over 3 end fraction
Image with alt text: start fraction 1 over 3 end fraction

Start Fraction 17 over 5 End Fraction
Image with alt text: Start Fraction 17 over 5 End Fraction

3

Answer 1

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.

Answer 2

pick one from above

Answer 3

Based on the given options, the closest value to 9√26 / 26 is:

Start Fraction 17 over 5 End Fraction