Question

5 multiple choice 1 point the midpoint of a line segment is (4,4), and one of the endpoints is (10,0). what are the coordinates of the other endpoint? (-2,8) (14,4) (7,2) (6,-4)

Explanation:

Step1: Recall the midpoint formula

The midpoint formula for two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(M = (\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\). Let the midpoint \(M=(4,4)\), one endpoint \((x_1,y_1)=(10,0)\) and the other endpoint \((x_2,y_2)\).

Step2: Solve for \(x_2\)

Using the \(x\) - coordinate of the midpoint formula: \(4=\frac{10 + x_2}{2}\). Multiply both sides by \(2\): \(8 = 10+x_2\). Then \(x_2=8 - 10=-2\).

Step3: Solve for \(y_2\)

Using the \(y\) - coordinate of the midpoint formula: \(4=\frac{0 + y_2}{2}\). Multiply both sides by \(2\): \(8=0 + y_2\). Then \(y_2 = 8\).

Answer:

\((-2,8)\) (corresponding to the first option)