Question

Find the coordinates of the other three vertices of the rectangle in the figure below:

The unit of length used in this centimetres. What is actual width and height of this rectangle?

Answer 1

Given: ABCO is a rectangle.

We know that in a rectangle, opposite sides are equal.

∴ AB = OC and AO = BC

The coordinates of point B are (4, 3).

Therefore, the perpendicular distance of point B from x-axis is 3 units and from y-axis is 4 units.

Point A of the given rectangle is lies on the y-axis. Therefore, its x-coordinate is 0.

Also, the perpendicular distance of point A from the origin = Perpendicular distance of point B from the x-axis = 3 units.

Therefore, the x-coordinate of point A is 0 and the y-coordinate is 3.

So, the coordinates of point A are (0, 3).

Point O is the origin of the rectangle. So, the coordinates of point O are (0, 0).

Point C of the given rectangle is lies on the x-axis. Therefore, its y-coordinate is 0.

The perpendicular distance of point C from the origin = Perpendicular distance of point B from the y-axis = 4 units.

Therefore, the x-coordinate of point C is 4 and the y-coordinate is 0.

So, the coordinates of point C are (4, 0).

Hence, the coordinates of the other three vertices of the given rectangle are (0, 3), (0, 0) and (4, 0).

Unit length used in the figure =

∴ Actual width of the rectangle =

Actual height of the rectangle =