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).

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)= ((x_(1)+x_(2) )/(2) , (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) =
`((-6+x_(2) )/(2), (8+y_(2) )/(2))`

For x value,

0 =
`(-6+x_(2) )/(2)`

0 = -6 +
`x_(2)`

`x_(2)` = 6

For y values,

0.5 =
`(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

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)