Question

M is the midpoint of AB¯. The coordinates of A are (2, 3) and the coordinates of M are (4.5, 6). What is the coordinate of B?

Answer 1

B = (7, 9)

Explanation:

Midpoint between two points

`\textsf{M}=\left((x_2+x_1)/(2),(y_2+y_1)/(2)\right)`

Where (x₁, y₁) and (x₂, y₂) are the endpoints.

Given:

• A = (2, 3)
• M = (4.5, 6)

Substitute the coordinates into the formula:

`\implies (x_M, y_M)=\left((x_B+x_A)/(2),(y_B+y_A)/(2)\right)`

`\implies (4.5, 6)=\left((x_B+2)/(2),(y_B+3)/(2)\right)`

`\implies (9,12)=\left(x_B+2,y_B+3\right)`

`\implies (9-2,12-3)=\left(x_B,y_B\right)`

`\implies (7,9)=\left(x_B,y_B\right)`

Therefore, the coordinates of B are (7, 9).