Question

5-47. at right is a graph of a periodic function and the line ( y = 5 ). one of the intersection points is ( (11.31, 5) ).
homework help
a. what is the period of the function?
b. use the symmetry of the graph to state the coordinates of the intersection labeled as point ( b ).
c. what are the coordinates of point ( c )?

Explanation:

Step1: Find period via distance B-C

Point C is at $x=0$, point B is at $x=20$. Period is the horizontal distance between two identical points on the wave.
$\text{Period} = 20 - 0 = 20$

Step2: Find point B using symmetry

Point A $(11.31,5)$ is halfway between C and B. Let $x_B$ be the x-coordinate of B. Use midpoint formula: $\frac{0 + x_B}{2} = 11.31$
$x_B = 11.31 \times 2 = 22.62$
Coordinates of B: $(22.62, 5)$

Step3: Find point C via period symmetry

Point A is 11.31 units right of C. Subtract the period from A's x-coordinate to get C's x-coordinate (since the function repeats every 20 units, moving left one period from A gives C).
$x_C = 11.31 - 20 = -8.69$
Coordinates of C: $(-8.69, 5)$

Answer:

a. $\boldsymbol{20}$
b. $\boldsymbol{(22.62, 5)}$
c. $\boldsymbol{(-8.69, 5)}$