Question

Point a is at (-6, 8) and point M is at (0, 0.5). Point M is the midpoint of point A and point B what are the coordinates of point B

Answer 1

The coordinates of point B is (6, -7), if the Point A is at (-6, 8) and point M is at (0, 0.5).

Step-by-step explanation:

The given is,

                A (-6, 8)

                M (0, 0.5)

                Where, A is first point

                             M is mid point

Step:1

          Formula for calculation of Mid point between two points,

                        $(x,y)= (\frac{x_{1}+x_{2} }{2} , \frac{y_{1}+y_{2} }{2} )$........................(1)

          Where,

                   A (-6, 8) - $( x_{1},y_{1} )$

                   M ( 0, 0.5) - $(x,y)$

           Substitute the values,

                     ( 0, 0.5) = $(\frac{-6+x_{2} }{2}, \frac{8+y_{2} }{2})$

           For x value,

                   0 = $\frac{-6+x_{2} }{2}$

                   0 = -6 + $x_{2}$

                  $x_{2}$ = 6

          For y values,

                  0.5 =  $\frac{8+y_{2} }{2}$

                     1 = 8 + $y_{2}$

                      $y_{2}$ = -7

Result:

          The coordinates of point B is (6, -7), if the Point A is at (-6, 8) and point M is at (0, 0.5).

Answer 2

Step-by-step explanation:

A is the first point  (-6,8) = (x₁,y₁)

M is a mid point  (0,0.5)

B is the end point   ( $x_{2} ,y_{2}$ )

Using the mid point formula

Mid point = { ( x₁ + x₂) / 2}  , { (y₁ + y₂ ) /2 }

Putting the values in the formula  -

( 0 , 0.5 ) =  ( -6 + x₂ ) /2 , ( 8 + y₂) /2

Evaluating x and y terms respectively

     $0 = (-6 + x_{2}) / 2\\x_{2} = 6$

x coordinate of point B is 6

   $0.5 =( 8 + y_{2} ) / 2\\y_{2} = -7$

y coordinate of point B is -7

Coordinates of point B is (6 , - 7)