Question

Point B is the midpoint of Segment AC. The coordinates of A are (-9,3) and the coordinates of B are (2,-3). What are the coordinates of C?

Answer 1

The coordinates of point C, the other endpoint of Segment AC, are (-13, -9).

Step-by-step explanation:

Point B is defined as the midpoint of Segment AC. The midpoint formula is expressed as (xₘ, yₘ) = ((x₁ + x₂)/2, (y₁ + y₂)/2), where (x₁, y₁) and (x₂, y₂) are the coordinates of the two endpoints, and (xₘ, yₘ) is the midpoint.

Given that B is the midpoint, with coordinates (2, -3), and A has coordinates (-9, 3), we can use the midpoint formula to find the coordinates of C. Let (x₃, y₃) represent the coordinates of C.

For the x-coordinate:

`\[ (2) = (-9 + x₃)/2 \]`

Solving for x₃, we get:

`\[ x₃ = 2 * 2 - (-9) = 13 \]`

For the y-coordinate:

`\[ (-3) = (3 + y₃)/2 \]`

Solving for y₃, we get:

\
`[ y₃ = -3 * 2 - 3 = -9 \]`

Therefore, the coordinates of point C are (-13, -9). In conclusion, the midpoint formula provides a straightforward method to find the coordinates of an endpoint when the midpoint and one endpoint are known. Applying this formula with precision allows us to determine that point C is located at (-13, -9), completing the information for Segment AC.