Questions: Find the midpoint of the line segment joining the points P₁ and P₂. P₁=(2,-4) ; P₂=(6,8) The midpoint of the line segment joining the points P₁ and P₂ is □ (Simplify your answer. Type an ordered pair.)

Find the midpoint of the line segment joining the points P₁ and P₂.
P₁=(2,-4) ; P₂=(6,8)

The midpoint of the line segment joining the points P₁ and P₂ is □
(Simplify your answer. Type an ordered pair.)

Transcript text: Find the midpoint of the line segment joining the points $P_{1}$ and $P_{2}$. \[ P_{1}=(2,-4) ; P_{2}=(6,8) \] The midpoint of the line segment joining the points $P_{1}$ and $P_{2}$ is $\square$ (Simplify your answer. Type an ordered pair.)

Solution

Solution Steps

Step 1: Identify the Given Points

The given points are $P_1(2, -4)$ and $P_2(6, 8)$.

Step 2: Apply the Midpoint Formula

The formula to find the midpoint $M$ of a line segment joining two points $P_1(x_1, y_1)$ and $P_2(x_2, y_2)$ is: \[M = \left( \frac{{x_1 + x_2}}{{2}}, \frac{{y_1 + y_2}}{{2}} \right)\]

Step 3: Substitute the Given Values into the Formula

Substituting the given values into the formula, we get: \[M = \left( \frac{2 + 6}{2}, \frac{-4 + 8}{2} \right) = (4, 2)\]