Question

`ABCD` is a rectangle with `B(-5, 0), C(7, 0)` and `D(7, 3)`. What are the coordinates of `A`?

Answer 1

A(-5, 3)

Explanation:

Since AB is parallel to CD and further AD is parallel to BC, We can easily find the coordinates of A as (-5, 3).

AB distance = CD distance = 3 units
BC distance = AD distance = 12 units

Area of this rectangle is 36 `units^2`
Perimeter of this rectangle is 30 units.

Answer 2

Let the coordinates of A be `(x,y)`
Since ABCD is a rectangle, its diagonals `AC and BD` will bisect each other.
The coordinates of mid point of `BD=((-5+7)/2,(0+3)/2)=(1,1.5)`

And the coordinates of mid point of `AC=((x+7)/2,(y+0)/2)`

So

`(x+7)/2=1`

`=>x=-5`

again

`(y+0)/2=1.5`

`=>y=3`

Hence the coordinates of A will be `(-5,3)`