Final answer:
The coordinates of the other endpoint D given a specific midpoint and one endpoint is found using the midpoint formula. So, the correct answer is option a. (15, -5).
Step-by-step explanation:
To find the coordinates of the other endpoint, D, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint M is the average of the coordinates of the two endpoints. So, we can use this formula to find the x-coordinate and y-coordinate of D.
Given that the endpoints are C(5,3) and the midpoint is M(10,-1), we can find the x-coordinate of D by doubling the x-coordinate of M and subtracting the x-coordinate of C. So, x-coordinate of D = (2 * 10) - 5 = 15.
To find the y-coordinate of D, we can apply the same process. y-coordinate of D = (2 * -1) - 3 = -5. Therefore, the coordinates of D are (15, -5). So, the correct answer is option a. (15, -5).