Three vertices of a rectangle abcd are a(3,1) b(-3,1) and c(-3,3). find the fourth vertex and the area of the rectangle

The Fourth vertex of the rectangle ABCD is (3, 3) and the area of the rectangle is 12 unit.

Solution:

Given three vertices of a rectangle are

A= (3, 1)

B= (-3, 1)

C= (-3, 3)  

Step 1:

The graph for this sum is attached below.

By looking at the graph we see that coordinates of D are (3, 3)  

We found the fourth vertex and now we can find the Area of rectangle.

Step 2:

The distance between B and C

We know the co-ordinates of B and C are B = (-3, 1) and C= (-3, 3)  

BC= (-3+3) + (3-1) = 2

Step 3:

The distance between D and C

We know the co-ordinates of D and C are (3, 3) and C= (-3, 3)  

DC= (-3-3) + (3-3) = 6

Step 4:

Area of ABCD rectangle = length breadth = DC BC

= 6 × 2  = 12 units  

Therefore area of Rectangle is 12 cm.

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2nd one in the first row is correct