Question

find the other endpoint given the midpoint and one of the endpoints.
① midpoint = (8.5, 5)
endpoint = (8, 2)
② midpoint = (-5.5, 3.5)
endpoint = (-6, 3)

Explanation:

Step1: Use mid - point formula

The mid - point formula for two points \((x_1,y_1)\) and \((x_2,y_2)\) is \((\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\). Let the unknown endpoint be \((x,y)\), the given mid - point \((-5.5,3.5)\) and one endpoint \((-6,3)\).
For the \(x\) - coordinate: \(-5.5=\frac{-6 + x}{2}\).

Step2: Solve for \(x\)

Multiply both sides by \(2\): \(-5.5\times2=-6 + x\), so \(-11=-6 + x\). Then \(x=-11 + 6=-5\).

Step3: Solve for \(y\)

For the \(y\) - coordinate: \(3.5=\frac{3 + y}{2}\). Multiply both sides by \(2\): \(3.5\times2=3 + y\), so \(7 = 3+y\). Then \(y=7 - 3 = 4\).

Answer:

The other endpoint is \((-5,4)\)