Questions: B has a midpoint at M(13.5,14). Point C is at (13,20). Find the coordinates of point B. Write the coordinates as decimals or integers.

Solution Steps

To find the coordinates of point \( B \), we can use the midpoint formula. The midpoint \( M \) of a line segment with endpoints \( B(x_1, y_1) \) and \( C(x_2, y_2) \) is given by: \[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] Given \( M(13.5, 14) \) and \( C(13, 20) \), we can set up equations to solve for \( x_1 \) and \( y_1 \) (the coordinates of point \( B \)).

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 \( B \).

Given the midpoint \( M(13.5, 14) \) and point \( C(13, 20) \), we use the midpoint formula to find the coordinates of point \( B \). 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 point \( B \) and \( (x_2, y_2) \) are the coordinates of point \( C \).

We set up the following equations based on the midpoint formula: \[ 13.5 = \frac{x_1 + 13}{2} \] \[ 14 = \frac{y_1 + 20}{2} \]

To find \( x_1 \), we solve the equation: \[ 13.5 = \frac{x_1 + 13}{2} \] Multiplying both sides by 2: \[ 27 = x_1 + 13 \] Subtracting 13 from both sides: \[ x_1 = 14 \]

To find \( y_1 \), we solve the equation: \[ 14 = \frac{y_1 + 20}{2} \] Multiplying both sides by 2: \[ 28 = y_1 + 20 \] Subtracting 20 from both sides: \[ y_1 = 8 \]

Final Answer