Questions: The midpoint M of QR has coordinates (6,7). Point R has coordinates (2,5). Find the coordinates of point Q. Write the coordinates as decimals or integers. Q=( , )

Solution Steps

To find the coordinates of point \( Q \), we can use the midpoint formula. The midpoint \( M \) of a line segment with endpoints \( Q(x_1, y_1) \) and \( R(x_2, y_2) \) is given by the formula:

\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]

Given the midpoint \( M(6, 7) \) and point \( R(2, 5) \), we can set up equations to solve for the coordinates of point \( Q(x_1, y_1) \).

1. Use the midpoint formula to set up equations for \( x_1 \) and \( y_1 \).
2. Solve these equations to find the coordinates of point \( Q \).

The midpoint \( M \) of a line segment with endpoints \( Q(x_1, y_1) \) and \( R(x_2, y_2) \) is given by:

\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]

Given \( M(6, 7) \) and \( R(2, 5) \), we can set up the following equations:

\[ 6 = \frac{x_1 + 2}{2} \] \[ 7 = \frac{y_1 + 5}{2} \]

Multiply both sides of the first equation by 2 to eliminate the fraction:

\[ 12 = x_1 + 2 \]

Subtract 2 from both sides:

\[ x_1 = 10 \]

Multiply both sides of the second equation by 2 to eliminate the fraction:

\[ 14 = y_1 + 5 \]

Subtract 5 from both sides:

\[ y_1 = 9 \]

Final Answer