Question

The midpoint M and one endpoint of CD are given:M(2,−1),C(−9,4)

Find the coordinates of the missing endpoint.

a) (13, -6)
b) (-5, -3)
c) (-5, 6)
d) (13, 2)

Answer 1

To find the missing endpoint D coordinates given midpoint M(2, -1) and endpoint C(-9, 4), we use the equations for the x and y coordinates of the midpoint, leading to the solution (13, -6) for endpoint D, which is option (a).

Step-by-step explanation:

The student's question pertains to finding the coordinates of the missing endpoint D of line segment CD given midpoint M and endpoint C. Since M is the midpoint, the coordinates of M are the averages of the coordinates of C and D. Therefore, we can set up equations to solve for the coordinates of D (Dx, Dy).

The formula for the midpoint (Mx, My) of a line segment with endpoints (Cx, Cy) and (Dx, Dy) is:

• Mx = (Cx + Dx)/2
• My = (Cy + Dy)/2

Using the given midpoint M(2, -1) and the endpoint C(-9, 4), we can set up our equations:

• 2 = (-9 + Dx)/2
• -1 = (4 + Dy)/2

Solving the first equation for Dx:

1. Multiply both sides by 2: 4 = -9 + Dx
2. Add 9 to both sides: Dx = 13

Solving the second equation for Dy:

1. Multiply both sides by 2: -2 = 4 + Dy
2. Subtract 4 from both sides: Dy = -6

Thus, the coordinates of endpoint D are (13, -6), which corresponds to option (a).