To determine the coordinates of R given that M(4, 2) is the midpoint of segment RS and the coordinates of S are (6, 1), we can use the midpoint formula. The midpoint formula is:
\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
where \((x_1, y_1)\) are the coordinates of R and \((x_2, y_2)\) are the coordinates of S.
Given:
- Midpoint M = (4, 2)
- Coordinates of S = (6, 1)
Let \(R = (x_1, y_1)\). Plugging in the known values into the midpoint formula, we get:
\[
4 = \frac{x_1 + 6}{2} \quad \text{and} \quad 2 = \frac{y_1 + 1}{2}
\]
First, solve for \(x_1\):
\[
4 = \frac{x_1 + 6}{2}
\]
Multiply both sides by 2 to clear the fraction:
\[
8 = x_1 + 6
\]
Subtract 6 from both sides:
\[
x_1 = 2
\]
Next, solve for \(y_1\):
\[
2 = \frac{y_1 + 1}{2}
\]
Multiply both sides by 2 to clear the fraction:
\[
4 = y_1 + 1
\]
Subtract 1 from both sides:
\[
y_1 = 3
\]
Therefore, the coordinates of R are (2, 3).
The correct answer is:
(2, 3)
9.
M(4, 2) is the midpoint of . The coordinates of S are (6, 1). What are the coordinates of R?
(1.5, 3)
(2, 3)
(5, 1.5)
(8, 0)
1 answer