Question

find the midpoint, m, of $overline{ab}$. a = (3, 1) b = (-1, -1) m = (?, ) m = ($\frac{x_1 + x_2}{2}$, $\frac{y_1 + y_2}{2}$)

Explanation:

Step1: Calculate x - coordinate of mid - point

Let \(A=(x_1,y_1)=(3,1)\) and \(B=(x_2,y_2)=(-1,-1)\). The formula for the x - coordinate of the mid - point \(M_x=\frac{x_1 + x_2}{2}\). Substitute \(x_1 = 3\) and \(x_2=-1\) into the formula: \(\frac{3+( - 1)}{2}=\frac{3 - 1}{2}=\frac{2}{2}=1\).

Step2: Calculate y - coordinate of mid - point

The formula for the y - coordinate of the mid - point \(M_y=\frac{y_1 + y_2}{2}\). Substitute \(y_1 = 1\) and \(y_2=-1\) into the formula: \(\frac{1+( - 1)}{2}=\frac{1 - 1}{2}=0\).

Answer:

\((1,0)\)