Question

Find the coordinates of the midpoint of the segment whose endpoints are H(9, 10) and
K(7, 6).
Find HK

Answer 1

mid point formula: $\text{coordinates of midpoint= }\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right) \\ \text{distance between two points= } \sqrt{(x_2-x_1)^2+(y_2-y_1)^2)}$

Answer 2

Answer:   The coordinate of the midpoint is m ( 8   ,   8)     and the distance HK is 4.5

Step-by-step explanation:

To find the coordinates of the point of the segment whose endpoints are H(9,10) and K(7,6), we simply use this formula;

m($x_{m}$ ,  $y_{m}$)   =   m( $\frac{x_{1} + x_{2} }{2}$     ,     $\frac{y_{1} + y_{2} }{2}$    )

                     

$x_{1}$  =  9      $y_{1}$  =  10          $x_{2}$  =   7          $y_{2}$   =   6

m($x_{m}$ ,  $y_{m}$)     =  m  ($\frac{9 + 7}{2}$            ,       $\frac{10 + 6}{2}$     )

   

                       = m ($\frac{16}{2}$         ,            $\frac{16}{2}$          )

                          =m (  8   ,     8)

The coordinate of the midpoint is m (  8   ,     8)

To find the distance HK,

let D = distance HK

D  =   √ $(x_{2} - x_{1} )^{2}$    +    $(y_{2} - y_{1}) ^{2}$

       =  √(7 - 9)²   +   (6 - 10)²

       =  √(-2)²   + (-4)²

      =  √4  +  16

       

       =√20

      = 4.5  

The distance HK is 4.5