Question

find the midpoint of the segment in the diagram. a (-1,1) b (-\frac{1}{2},-\frac{1}{2}) c (-\frac{1}{2},\frac{1}{2}) d (\frac{5}{2},-\frac{5}{2}) e (\frac{5}{2},\frac{5}{2})

Explanation:

Step1: Identify endpoints

Let the endpoints of the line - segment be \((x_1,y_1)\) and \((x_2,y_2)\). From the graph, if one endpoint is \((-2,3)\) and the other is \((2, - 2)\).

Step2: Apply mid - point formula

The mid - point formula is \(M=(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\). Substitute \(x_1=-2,y_1 = 3,x_2 = 2,y_2=-2\) into the formula. For the x - coordinate of the mid - point: \(\frac{-2 + 2}{2}=\frac{0}{2}=0\). For the y - coordinate of the mid - point: \(\frac{3+( - 2)}{2}=\frac{3 - 2}{2}=\frac{1}{2}\). So the mid - point is \((0,\frac{1}{2})\).

Answer:

\((0,\frac{1}{2})\)