Question

find the coordinates of the midpoint of a segment with the given endpoints.

1. ( k(-9,3), h(5,7) )
2. ( w(-12,-7), t(-8,-4) )

find the missing endpoint if ( e ) is the midpoint of ( overline{d f} ).

Explanation:

Step1: Recall the mid - point formula

The mid - point formula for two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\).

Step2: For problem 15

Given \(K(-9,3)\) and \(H(5,7)\).
For the \(x\) - coordinate of the mid - point: \(\frac{-9 + 5}{2}=\frac{-4}{2}=-2\).
For the \(y\) - coordinate of the mid - point: \(\frac{3+7}{2}=\frac{10}{2} = 5\).

Step3: For problem 16

Given \(W(-12,-7)\) and \(T(-8,-4)\).
For the \(x\) - coordinate of the mid - point: \(\frac{-12+( - 8)}{2}=\frac{-12 - 8}{2}=\frac{-20}{2}=-10\).
For the \(y\) - coordinate of the mid - point: \(\frac{-7+( - 4)}{2}=\frac{-7 - 4}{2}=\frac{-11}{2}=-5.5\).

Answer:

1. The mid - point is \((-2,5)\).
2. The mid - point is \((-10,-5.5)\).