Question

What is the midpoint of the segment that extends 15 units from (0,0) at a 45∘ angle?

A) ((7.5, 7.5))
B) ((10, 10))
C) ((10.6, 10.6))
D) ((7.5√2, 7.5√2))

Answer 1

C) ((10.6, 10.6)). The midpoint of the segment that extends 15 units from (0,0) at a 45∘ angle is ((10.6, 10.6)).

Step-by-step explanation:

To find the midpoint of the segment extending 15 units from (0,0) at a 45∘ angle, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint of a line segment are the average of the coordinates of the two endpoints. In this case, the endpoint coordinates are (0,0) and the endpoint of the segment 15 units away at a 45∘angle.

First, we find the x-coordinate by using the formula: (x1 + x2) / 2. Since the x-coordinate of the starting point (0,0) is 0, we can just use the x-coordinate of the endpoint. The x-coordinate of the endpoint can be found using the cosine function: x = 15 * cos(45∘) = 10.6

Next, we find the y-coordinate by using the formula: (y1 + y2) / 2. Since the y-coordinate of the starting point (0,0) is 0, we can just use the y-coordinate of the endpoint. The y-coordinate of the endpoint can be found using the sine function: y = 15 * sin(45∘) = 10.6

Therefore, the midpoint of the segment is ((10.6, 10.6)), which corresponds to answer choice C.