Question

- In a classroom, 4 friends are
Das shown in Fig. 7.8. Champa
seated at the points A, B, C and
and Chameli walk into the class
and after observing for a few
minutes Champa asks Chameli.
"Don't you think ABCD is a
square?" Chameli disagrees.
Using distance formula, find
which of them is correct.​

Answer 1

Answer:

Step-by-step explanation: By using the distance formula

Finding AB

x1= 3 , y1= 4

x2= 6 , y2= 7

The coordinates of the points:

A(3,4),\ B(6,7),\ C(9,4),\ and\ D(6,1) are the positions of 4 friends.

The distance between two points A(x_{1},y_{1}), \ and\ B(x_{2},y_{2}) is given by:

D = \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}

Hence,

AB = \sqrt{(3-6)^2+(4-7)^2} = \sqrt{9+9} = \sqrt{18} = 3\sqrt2

BC = \sqrt{(6-9)^2+(7-4)^2} = \sqrt{9+9} = \sqrt{18} = 3\sqrt2

CD = \sqrt{(9-6)^2+(4-1)^2} = \sqrt{9+9} = \sqrt{18} = 3\sqrt2

AD= \sqrt{(3-6)^2+(4-1)^2} = \sqrt{9+9} = \sqrt{18} = 3\sqrt2

And the lengths of diagonals:

AC = \sqrt{(3-9)^2+(4-4)^2} =\sqrt{36+0} = 6

BD = \sqrt{(6-6)^2+(7-1)^2} =\sqrt{36+0} = 6

So, here it can be seen that all sides of quadrilateral ABCD are of the same lengths and diagonals are also having the same length.

Therefore, quadrilateral ABCD is a square and Champa is saying right.