Question

In the coordinate plane, three vertices of rectangle ABCD are A(0, 0), B(0, a), and D(b, 0). What are the coordinates of point C?

Answer 1

Coordinates of `C` are `(b,a)`

Explanation:

As `A(0,0)` and `B(0,a)` have abscissa as `0`, they fall on `y`-axis. Similarly `A(0,0)` and `D(b,0)` have ordinate as `0`, they fall on `x`-axis.

As such `BC`||`AD` i.e. parallel to `x` axis and as such `B` and `D` must have common ordinate i.e. `a`.

Also `CD`||`AB` i.e. parallel to `y` axis and as such `C` and `D` must have common abcissa i.e. `b`.

Hence, coordinates of `C` are `(b,a)`