Question

find the midpoint, m, of ab. a = (2,1) b = (-4,7) m = (?, ) m = (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})

Explanation:

Step1: Substitute coordinates into formula

Given \(A=(x_1,y_1)=(2,1)\) and \(B=(x_2,y_2)=(-4,7)\), use the mid - point formula \(M = (\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\).
So, \(x\) - coordinate of \(M\) is \(\frac{2+(-4)}{2}\), and \(y\) - coordinate of \(M\) is \(\frac{1 + 7}{2}\).

Step2: Calculate \(x\) - coordinate

$$\frac{2+(-4)}{2}=\frac{2 - 4}{2}=\frac{-2}{2}=-1$$

Step3: Calculate \(y\) - coordinate

$$\frac{1 + 7}{2}=\frac{8}{2}=4$$

Answer:

$(-1,4)$