The coordinates of midpoint $M$ and endpoint $C$ of a segment are $M(25.4,60.1)$ and $C(18.3,72.5)$. Find the coordinates of the other endpoint.

Use the midpoint formula to set up equations for the x and y coordinates.
Solve the equation for x: x = 2 × 25.4 − 18.3 = 32.5 .
Solve the equation for y: y = 2 × 60.1 − 72.5 = 47.7 .
State the coordinates of the other endpoint: ( 32.5 , 47.7 ) ​ .

Explanation

Problem Analysis We are given the midpoint M ( 25.4 , 60.1 ) and one endpoint C ( 18.3 , 72.5 ) of a line segment. We need to find the coordinates of the other endpoint, which we'll call A ( x , y ) . The midpoint formula tells us that the coordinates of the midpoint are the average of the coordinates of the endpoints.

Applying the Midpoint Formula Using the midpoint formula, we have: 2 x + 18.3 ​ = 25.4 2 y + 72.5 ​ = 60.1

Solving for x Now, we solve for x :
x + 18.3 = 2 × 25.4 x + 18.3 = 50.8 x = 50.8 − 18.3 x = 32.5

Solving for y Next, we solve for y :
y + 72.5 = 2 × 60.1 y + 72.5 = 120.2 y = 120.2 − 72.5 y = 47.7

Final Answer Therefore, the coordinates of the other endpoint are ( 32.5 , 47.7 ) .


Examples
In computer graphics, if you know the midpoint of a line and one endpoint, you can find the other endpoint to draw lines and shapes correctly. This is useful in creating images and animations.

Answered by GinnyAnswer | 2025-07-03

The coordinates of the other endpoint A, using the midpoint M(25.4, 60.1) and endpoint C(18.3, 72.5), are (32.5, 47.7). This is calculated using the midpoint formula for both the x and y coordinates. The calculations show that x = 32.5 and y = 47.7.
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Answered by Anonymous | 2025-07-04