Question

what is the midpoint of the line graphed on the coordinate plane below? (1,4) (-1,-1) (2,6) (-4,9)

Explanation:

Step1: Identify endpoints

Assume the endpoints of the line segment are \(A(x_1,y_1)\) and \(B(x_2,y_2)\). From the graph, if \(A(- 6,-9)\) and \(B(4,10)\)

Step2: Use mid - point formula

The mid - point formula is \(M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\). Substitute \(x_1=-6,x_2 = 4,y_1=-9,y_2 = 10\) into the formula. For the x - coordinate of the mid - point: \(\frac{-6 + 4}{2}=\frac{-2}{2}=-1\). For the y - coordinate of the mid - point: \(\frac{-9+10}{2}=\frac{1}{2}=0.5\). However, if we assume a more approximate reading, if we consider the closest grid - point values, say \(A(-6,-9)\) and \(B(4,7)\)

• Calculate x - coordinate of mid - point

\(x=\frac{-6 + 4}{2}=\frac{-2}{2}=-1\)

• Calculate y - coordinate of mid - point

\(y=\frac{-9 + 7}{2}=\frac{-2}{2}=-1\)

Answer:

(-1,-1)