Questions: The endpoints of CD are C(-4,7) and D(0,-3). The coordinates of the midpoint M of CD are (-2,2).

Transcript text: The endpoints of $\overline{C D}$ are $C(-4,7)$ and $D(0,-3)$. The coordinates of the midpoint $M$ of $\overline{C D}$ are $(-2,2)$.

Solution

Solution Steps

To find the midpoint $ M $ of a line segment with endpoints $ C(x_1, y_1) $ and $ D(x_2, y_2) $, we use the midpoint formula: \[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]

Given the endpoints $ C(-4, 7) $ and $ D(0, -3) $, we can plug these values into the formula to find the coordinates of the midpoint.

Step 1: Identify the Coordinates of the Endpoints

The endpoints of the line segment are given as: $ C(-4, 7) $ and $ D(0, -3) $.

Step 2: Apply the Midpoint Formula

To find the midpoint $ M $ of the line segment with endpoints $ C(x_1, y_1) $ and $ D(x_2, y_2) $, we use the midpoint formula: \[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]

Step 3: Substitute the Coordinates into the Formula

Substitute $ x_1 = -4 $, $ y_1 = 7 $, $ x_2 = 0 $, and $ y_2 = -3 $ into the formula: \[ M_x = \frac{-4 + 0}{2} = \frac{-4}{2} = -2.0 \] \[ M_y = \frac{7 + (-3)}{2} = \frac{4}{2} = 2.0 \]

Final Answer

$\boxed{M = \left( -2, 2 \right)}$

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!