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Sagot :
Answer:
Step-by-step explanation:
To find the coordinates of point \( A \), given that point \( C(4, 6) \) is the midpoint of line segment \( AB \) and point \( B(2, 8) \), we can use the midpoint formula.
The midpoint formula is:
\[
\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
Here, \( C(4, 6) \) is the midpoint, \( B(2, 8) \) is one endpoint, and \( A(x_1, y_1) \) is the other endpoint we need to find.
Using the midpoint formula:
\[
\frac{x_1 + 2}{2} = 4 \quad \text{and} \quad \frac{y_1 + 8}{2} = 6
\]
Solving for \( x_1 \):
\[
\frac{x_1 + 2}{2} = 4 \implies x_1 + 2 = 8 \implies x_1 = 6
\]
Solving for \( y_1 \):
\[
\frac{y_1 + 8}{2} = 6 \implies y_1 + 8 = 12 \implies y_1 = 4
\]
Therefore, the coordinates of point \( A \) are \( (6, 4) \).
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