Three vertices of a rectangle ABCD are A(3, 1), B(–3, 1) and C(–3, 3). Plot these points on a graph paper and find the coordinates of the fourth vertex D.
Question:

Three vertices of a rectangle ABCD are A(3, 1), B(–3, 1) and C(–3, 3). Plot these points on a graph paper and find the coordinates of the fourth vertex D. Also, find the area of rectangle ABCD.

 

Solution:

Let A(3, 1), B(–3, 1) and C(–3, 3) be three vertices of a rectangle ABCD.

Let A(3, 1), B(–3, 1) and C(–3, 3) be three vertices of a rectangle ABCD.

Abscissa of D = Abscissa of A = 3.
Ordinate of D = Ordinate of C = 3.

∴ coordinates of D are (3, 3).

AB = (BP + PA) = (3 + 3) units = 6 units.
BC = (OQ – OP) = (3 – 1) units = 2 units.

Ar(rectangle ABCD) = (AB × BC)
                                  = (6 × 2) sq. units
                                  = 12 sq. units

Hence, the area of rectangle ABCD is 12 square units.

 

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