Question

Given AB¯¯¯¯¯¯¯¯AB¯ where A(4, 0)A(4, 0)and M(2, 1.5)M(2, 1.5) and M is the midpoint of AB¯¯¯¯¯¯¯¯AB¯ . The coordinates of B would be

Answer 1

`B = (0,3)`

Step-by-step explanation:

Given

`A=(4,0)`

`M = (2,1.5)`

Required

Find B

Since M is the midpoint of AB, we make use of midpoint formula to solve this question

`M(x,y) = ((x_1+x_2)/(2).(y_1+y_2)/(2))`

Where

`A(x_1,y_1) = (4,0)`

`M(x,y) = (2,1.5)`

So, we have:

`(2,1.5) = ((4+x_2)/(2),(0+y_2)/(2))`

Multiply through by 2

`(4,3) = (4+x_2,0+y_2)`

`(4,3) = (4+x_2,y_2)`

By comparison:

`4 = 4 + x_2` and
`3 = y_2`

Solve for x2

`4 = 4 + x_2`

`x_2=4-4`

`x_2=0`

`y_2 = 3`

Hence, the coordinates of B is:
`(0,3)`