Three vertices of a rectangle are A(2, -1), B(2, 7) and C(4, 7). Plot these points on a graph and hence use it to find the co-ordinates of the fourth vertex D. Also find the co-ordinates of

(i) the mid-point of BC

(ii) the mid-point of CD

(iii) the point of intersection of the diagonals.

What is the area of the rectangle ?

In graph,

1 block = 1 unit.

Steps of construction :

1. Plot the points A(2, -1), B(2, 7) and C(4, 7) on graph.

2. Join AB and BC.

3. Measure AB. Draw a line segment CD, from point C parallel to y-axis.

4. Measure BC. Draw a line segment AD, from point A parallel to x-axis.

5. Mark F and G mid-point of BC and CD respectively.

6. Join AC and BD diagonals of rectangle.

7. Mark E as the point of intersection of diagonals.

From graph,

Coordinates of D = (4, -1).

(i) From graph,

F is the mid-point of BC and F = (3, 7).

Hence, coordinates of mid-point of BC = (3, 7).

(ii) From graph,

G is the mid-point of CD and G = (4, 3).

Hence, coordinates of mid-point of CD = (4, 3).

(iii) From graph,

E is the point of intersection of diagonals.

Hence, point of intersection of the diagonals = (3, 3).

From graph,

AB = 8 units and BC = 2 units.

Area of the rectangle ABCD = length × breadth

= AB × BC

= 8 × 2

= 16 sq. units.

Hence, the area of the rectangle = 16 sq. units.