Question

1. (overline{jl}) has endpoints (j(8,10)) and (l(20,5)). point (k) has coordinates ((13,9)).

a. is point (k) the midpoint of (overline{jl})? explain how you know.
b. how could you check that your answer to part a is reasonable?

1. find the coordinates of the midpoint of (overline{de}).
2. what are the coordinates of the midpoint of the segment with endpoints at ((-3,-4)) and ((5,8))?

a. ((1,2)) b. ((2,4)) c. ((4,6)) d. ((8,12))

Explanation:

18a.

Step1: Use mid - point formula

The mid - point formula for two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\). For \(J(8,10)\) and \(L(20,5)\), \(x=\frac{8 + 20}{2}=\frac{28}{2}=14\), \(y=\frac{10+5}{2}=\frac{15}{2}=7.5\).

Step2: Compare with point \(K\)

Point \(K\) has coordinates \((13,9)\). Since \(13
eq14\) and \(9
eq7.5\), point \(K\) is not the mid - point of \(\overline{JL}\).

Step1: Calculate distances

Use the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Calculate \(JK=\sqrt{(13 - 8)^2+(9 - 10)^2}=\sqrt{25 + 1}=\sqrt{26}\), \(KL=\sqrt{(20 - 13)^2+(5 - 9)^2}=\sqrt{49+16}=\sqrt{65}\).

Step2: Check mid - point property

If \(K\) were the mid - point, \(JK = KL\). But \(\sqrt{26}
eq\sqrt{65}\), so the answer in part (a) is reasonable.

Step1: Identify coordinates

From the graph, \(D(- 4,3)\) and \(E(3,-1)\).

Step2: Apply mid - point formula

\(x=\frac{-4 + 3}{2}=-\frac{1}{2}\), \(y=\frac{3+( - 1)}{2}=1\).

Answer:

No, point \(K\) is not the mid - point of \(\overline{JL}\).

18b.