Mccarthy Lewis
06/23/2023 · Junior High School
If point C is the midpoint of segment AB, and A is at (2, 3) and B is at (8, 7), what are the coordinates of point C?
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Step-by-step Solution
To find the coordinates of the midpoint \( C \) of segment \( AB \), we can use the midpoint formula, which is given by:
\[
C = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
where \( (x_1, y_1) \) are the coordinates of point \( A \) and \( (x_2, y_2) \) are the coordinates of point \( B \).
Given:
- Point \( A \) is at \( (2, 3) \) (so \( x_1 = 2 \) and \( y_1 = 3 \))
- Point \( B \) is at \( (8, 7) \) (so \( x_2 = 8 \) and \( y_2 = 7 \))
Now, we can substitute these values into the midpoint formula:
\[
C = \left( \frac{2 + 8}{2}, \frac{3 + 7}{2} \right)
\]
Calculating the x-coordinate:
\[
\frac{2 + 8}{2} = \frac{10}{2} = 5
\]
Calculating the y-coordinate:
\[
\frac{3 + 7}{2} = \frac{10}{2} = 5
\]
Thus, the coordinates of point \( C \) are:
\[
C = (5, 5)
\]
Therefore, the coordinates of point \( C \) are \( \boxed{(5, 5)} \).
Quick Answer
The coordinates of point \( C \) are \( (5, 5) \).
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