Question

The coordinate of the midpoint of segment AB is (-3, 2). Find the coordinate of A if the coordinate of B is (0, 2). A =

Answer 1

The midpoint of a line segment is just the average of the coordinates of the endpoints.

(0+x)/2=-3 and (2+y)/2=2

x=-6 and 2+y=4

x=-6 and y=2

So point B is (-6,2)

Answer 2

A= (-6, 2)

Explanation:

Let (
`x_(1)`
`y_(1)`) be the coordinates of A , let (
`x_(2)` ,
`y_(2)`) be the coordinate of B

and let (
`x_(m)` ,
`y_(m)`) be the midpoints of segment AB

To find the coordinates of A, we simply use the formula for calculating mid-points of segment

(
`x_(m)` ,
`y_(m)`) =
`((x_(1) + x_(2) )/(2), (y_(1) + y_(2) )/(2))`

From the formula above;

`x_(m)` =
`x_(1)` +
`x_(2)` / 2 ---------------(1)

Similarly

`y_(m)` =
`y_(1)` +
`y_(2)` / 2 --------(2)

From the question given;

(
`x_(m)` ,
`y_(m)`) = (-3, 2) which implies:
`x_(m)`= -3 and
`y_(m)`= 2

similarly (
`x_(2)` ,
`y_(2)`) = (0,2) this implies that
`x_(2)` = 0 and
`y_(2)` =2

From equation (1)

`x_(m)` =
`x_(1)` +
`x_(2)` / 2

we substitute
`x_(m)`= -3 and
`x_(2)` = 0 into equation (1) to get
`x_(1)`

`x_(m)` =
`x_(1)` +
`x_(2)` / 2

-3 =
`x_(1)` + 0 / 2

cross multiply

`x_(1)` + 0 = -3 × 2

`x_(1)` = -6

Also;

We substitute;
`y_(m)`= 2 and
`y_(2)` =2 into equation (2)

`y_(m)` =
`y_(1)` +
`y_(2)` / 2 --------(2)

2 =
`y_(1)` + 2 / 2

cross multiply

`y_(1)` + 2 = 2 × 2

`y_(1)` + 2 = 4

subtract 2 from both-side of the equation

`y_(1)` + 2 -2 = 4 -2

`y_(1)` = 2

`x_(1)` = -6 and
`y_(1)` = 2

Therefore; Coordinate of A (
`x_(1)`
`y_(1)`) = (-6, 2)