Questions: PQ has a midpoint at M(-0.5,3.5). Point Q is at (-18,-8). Find the coordinates of point P. Write the coordinates as decimals or integers. P=( , )

Transcript text: $\overline{P Q}$ has a midpoint at $M(-0.5,3.5)$. Point $Q$ is at $(-18,-8)$. Find the coordinates of point $P$. Write the coordinates as decimals or integers. P=(\square, \square)

Solution

Solution Steps

To find the coordinates of point $ P $, we can use the midpoint formula. The midpoint $ M $ of a line segment with endpoints $ P(x_1, y_1) $ and $ Q(x_2, y_2) $ is given by: \[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] Given the midpoint $ M(-0.5, 3.5) $ and point $ Q(-18, -8) $, we can set up equations to solve for the coordinates of point $ P $.

Solution Approach

Use the midpoint formula to set up equations for the x and y coordinates.
Solve these equations to find the coordinates of point $ P $.

Step 1: Set Up the Midpoint Formula

Given the midpoint $ M(-0.5, 3.5) $ and point $ Q(-18, -8) $, we use the midpoint formula: \[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] where $ P(x_1, y_1) $ and $ Q(x_2, y_2) $.

Step 2: Solve for $ x_1 $

Using the x-coordinates: \[ -0.5 = \frac{x_1 + (-18)}{2} \] Multiply both sides by 2: \[ -1 = x_1 - 18 \] Add 18 to both sides: \[ x_1 = 17 \]

Step 3: Solve for $ y_1 $

Using the y-coordinates: \[ 3.5 = \frac{y_1 + (-8)}{2} \] Multiply both sides by 2: \[ 7 = y_1 - 8 \] Add 8 to both sides: \[ y_1 = 15 \]