Question

question 7 of 25

the black figure is an ellipse, and the black line segment is its major axis. what is the length of the blue line segment?

a. 41.7
b. 20.3
c. 21.3
d. 10.7

Explanation:

Identify the given values and geometric properties

We are given an ellipse with a major axis of length \(2a = 31\).
A point on the ellipse is connected to both foci.
The distance from this point to the upper focus (red segment) is \(d_1 = 10.7\).
The distance from this point to the lower focus (blue segment) is \(d_2\).

Apply the definition of an ellipse

An ellipse is the locus of points such that the sum of the distances to the two foci is constant and equal to the length of the major axis:

$$d_1 + d_2 = 2a$$

Solve for the unknown length

Substitute the known values into the equation:

$$10.7 + d_2 = 31$$

$$d_2 = 31 - 10.7$$

$$d_2 = 20.3$$

Answer:

• A. 41.7
• B. 20.3 (Correct answer)
• C. 21.3
• D. 10.7