Question

part ii
1 what are the coordinates of the mid - point of the line segment with endpoints (2, - 5) and (8,3)?
2 the endpoints of $overline{cd}$ are $c(-2,-4)$ and $d(6,2)$. what are the coordinates of the mid - point of $overline{cd}$?
3 a line segment has endpoints $a(7,-1)$ and $b(-3,3)$. what are the coordinates of the mid - point of $overline{ab}$?
part iii
17 one endpoint of a line segment is $(6,2)$. the mid - point of the segment is $(2,0)$. find the coordinates of the other endpoint. the use of the grid is optional.
exit ticket: regents - ready question! show all calculations.
19 the endpoints of $overline{ab}$ are $a(3,-4)$ and $b(7,2)$. determine and state the length of $overline{ab}$ in simplest radical form.

Explanation:

1.

Step1: Recall mid - point formula

The mid - point formula for two points \((x_1,y_1)\) and \((x_2,y_2)\) is \((\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\). For endpoints \((2,-5)\) and \((8,3)\), \(x_1 = 2\), \(y_1=-5\), \(x_2 = 8\), \(y_2 = 3\).

Step2: Calculate x - coordinate of mid - point

\(x=\frac{2 + 8}{2}=\frac{10}{2}=5\)

Step3: Calculate y - coordinate of mid - point

\(y=\frac{-5 + 3}{2}=\frac{-2}{2}=-1\)

Step1: Identify values for mid - point formula

For endpoints \(C(-2,-4)\) and \(D(6,2)\), \(x_1=-2\), \(y_1 = - 4\), \(x_2 = 6\), \(y_2 = 2\).

Step2: Compute x - coordinate of mid - point

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

Step3: Compute y - coordinate of mid - point

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

Step1: Apply mid - point formula values

For endpoints \(A(7,-1)\) and \(B(-3,3)\), \(x_1 = 7\), \(y_1=-1\), \(x_2=-3\), \(y_2 = 3\).

Step2: Find x - coordinate of mid - point

\(x=\frac{7+( - 3)}{2}=\frac{7 - 3}{2}=\frac{4}{2}=2\)

Step3: Find y - coordinate of mid - point

\(y=\frac{-1 + 3}{2}=\frac{2}{2}=1\)

Answer:

\((5,-1)\)

2.