Question

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)

Answer 1

[AI-generated answer — Bot GPT-4o]

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)