Question

What are the coordinates of the other endpoint C if M is the midpoint of segment BC with B(-5, -4) and M(1,-5)?

A) (7, -6)
B) (-7, -6)
C) (-7, -3)
D) (7, -3)

Answer 1

To find the coordinates of the other endpoint C, the midpoint formula is used, resulting in C's coordinates being (7, -6).

Step-by-step explanation:

The student is asking how to find the coordinates of the other endpoint C of a line segment BC given that M is the midpoint and the coordinates of B and M are provided. The midpoint formula, which states that the midpoint M's coordinates are the averages of the endpoints' coordinates, will be used to solve this problem:

If M is the midpoint of BC, and B has coordinates (-5, -4), and M has coordinates (1, -5), then using the midpoint formula we can find C by solving for C's x and y coordinates:

• Mx = (Bx + Cx) / 2
• My = (By + Cy) / 2

Plugging in the known values we get:

• 1 = (-5 + Cx) / 2
• -5 = (-4 + Cy) / 2

Solving the equations for Cx and Cy gives us:

• Cx = 2 * 1 + 5 = 7
• Cy = 2 * (-5) + 4 = -6

Therefore, the coordinates of the other endpoint C are (7, -6).