Question

In the standard (x,y) coordinate plane, point M with coordinates (5,4) is the midpoint of AB, and B has coordinates (7,3). What are the coordinates of A ?

Answer 1

Coordinates of A are `(3,5)`

Explanation:

In a segment if `A(x_1,y_1)` and `B(x_2,y_2)` are coordinates of its end points, the coordinates of midpoint `M` are `(x_1+x_2)/2,(y_1+y_2)/2`.

Now we are given `A(x_1,y_1)` and `B(7,3)`, hence midpoint is `(x_1+7)/2,(y_1+3)/2`, but midpoint is given to be `(5,4)`.

Hence `(x_1+7)/2=5` i.e. `x_1+7=5xx2=10` and `x_1=10-7=3`

and `(y_1+3)/2=4` i.e. `y_1+3=4xx2=8` and `x_1=8-3=5`

Hence, coordinates of A are `(3,5)`