Question

The midpoint of BC is M(2, 7). One endpoint is B(0, 4). Find the coordinates of the other endpoint C."

Option 1: C(4, 10)
Option 2: C(2, 7)
Option 3: C(0, 1)
Option 4: C(6, 13)

Answer 1

To find the coordinates of endpoint C, the midpoint formula is used to average the coordinates of B and C. Solving the equations using the midpoint M(2, 7) and endpoint B(0, 4), the coordinates of C are determined to be C(4, 10).

Step-by-step explanation:

The student is asking how to find the coordinates of the other endpoint C given that the midpoint of BC is M(2, 7) and one endpoint is B(0, 4). To solve this, we can use the midpoint formula which states that the midpoint is the average of the endpoints. Since M is the midpoint, we have:

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

Plug the given coordinates into the equations:

1. 2 = (0 + Cx) / 2
2. 7 = (4 + Cy) / 2

Solving these equations, we find:

1. Cx = 2 * 2 = 4
2. Cy = 2 * 7 - 4 = 10

Therefore, the coordinates of point C are C(4, 10), which corresponds to Option 1.