Question

The midpoint of \overline{\text{AB}}

AB
is M(-5, -2)M(−5,−2). If the coordinates of AA are (-3, 4)(−3,4), what are the coordinates of BB?

Answer 1

The coordinates of b are: B=(-7,-8)

Explanation:

We are given the coordinates of the midpoint of
`\overline{\text{AB}}` as M=(-5,-2).

We are also given the coordinates of A=(-3,4). The question requires us to calculate the coordinates of the other endpoint B.

Let (xb,yb) the coordinates of B. The coordinates of the midpoint can be calculated as follows:

`\displaystyle x_m=(x_a+x_b)/(2)`

`\displaystyle y_m=(y_a+y_b)/(2)`

We know xa=-3 and xm=-5. Solve the first equation for xb:

`2x_m=x_a+x_b\Rightarrow x_b=2x_m-x_a`

Substituting:

`x_b=2\cdot (-5)-(-3)=-10+3`

`x_b=-7`

We can solve the second equation for xb and get:

`y_b=2y_m-y_a`

Since ya=4 and ym=-2, then:

`y_b=2\cdot (-2)-(4)=-4-4`

`y_b=-8`

Thus, the coordinates of b are: B=(-7,-8)