Question

Plot the points a ( 2,3) , B ( 2,1) C( 0,1) and D ( 0,3) . Join the points and identify the figure obtained . Find its perimeter .

Answer 1

$\large\underline{\sf{Solution-}}$

Given coordinates are

• Coordinates of A be (2, 3)

• Coordinates of B (2, 1)

• Coordinates of C (0, 1)

• Coordinates of D (0, 3).

[ Please see the attachment ].

From graph we concluded that

• AB = 2 units

• BC = 2 units

• CD = 2 units

• DA = 2 units

Also,

• AB is Perpendicular to BC.

• BC is perpendicular to CD

• CD is perpendicular to DA

• DA is perpendicular to AB.

It implies, AB = BC = CD = DA = 2 units.

As we know that,

In a quadrilateral, if all the 4 sides are equal and angle between the sides is 90°, then quadrilateral is a square.

So, this figure, ABCD is a square.

Now, Perimeter of a square = 4 × side = 4 × 2 = 8 units.

Let's solve one more problem now!!.

Question:- Plot the points A (3,0) , B ( 5, 0) C( 5, 5) and D ( 3, 5) . Join the points and identify the figure obtained . Find its perimeter.

Solution :-

Given coordinates are

• Coordinates of A be (3, 0)

• Coordinates of B (5, 0)

• Coordinates of C (5, 5)

• Coordinates of D (3, 5).

[ Please see the attachment ].

From graph we concluded that

• AB = 2 units

• BC = 5 units

• CD = 2 units

• DA = 5 units

Also,

• AB is Perpendicular to BC.

• BC is perpendicular to CD

• CD is perpendicular to DA

• DA is perpendicular to AB.

It implies, AB = CD = 2 units and BC = DA = 5 units.

As we know that,

In a quadrilateral, if pair of opposite sides are equal and angle between the sides is 90°, then quadrilateral is a rectangle.

So, this figure, ABCD is a rectangle.

Now, Perimeter of a rectangle = 2(AB + BC) =2(2+5)= 14 units.