Questions: Find the midpoint of the line segment joining the points P₁ and P₂. P₁=(y, 2) ; P₂=(0,3) A. (y, 5/2) B. (-y/2, 1) C. (y, 5) D. (y/2, 5/2)

Transcript text: Find the midpoint of the line segment joining the points $\mathrm{P}_{1}$ and $\mathrm{P}_{2}$. $P_{1}=(y, 2) ; P_{2}=(0,3)$ A. $\left(y, \frac{5}{2}\right)$ B. $\left(-\frac{y}{2}, 1\right)$ C. $(y, 5)$ D. $\left(\frac{y}{2}, \frac{5}{2}\right)$

Solution

Solution Steps

To find the midpoint of a line segment joining two points $ P_1 $ and $ P_2 $, we use the midpoint formula: \[ \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] Given $ P_1 = (y, 2) $ and $ P_2 = (0, 3) $, we substitute these coordinates into the formula to find the midpoint.

Step 1: Identify the Coordinates of the Points

The coordinates of the points are given as: \[ P_1 = (y, 2) \] \[ P_2 = (0, 3) \]

Step 2: Use the Midpoint Formula

The formula for the midpoint $ M $ of a line segment joining two points $ (x_1, y_1) $ and $ (x_2, y_2) $ is: \[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]

Step 3: Substitute the Coordinates into the Midpoint Formula

Substitute $ P_1 = (y, 2) $ and $ P_2 = (0, 3) $ into the midpoint formula: \[ M = \left( \frac{y + 0}{2}, \frac{2 + 3}{2} \right) \]

Step 4: Simplify the Expression

Simplify the expression to find the coordinates of the midpoint: \[ M = \left( \frac{y}{2}, \frac{5}{2} \right) \]

Final Answer

The midpoint of the line segment joining the points $ P_1 $ and $ P_2 $ is: \[ \boxed{\left( \frac{y}{2}, \frac{5}{2} \right)} \] Thus, the answer is D.

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!