Mathematics: Iam having a total mind blank right now.write a coordinate proof for the following theorem. if a quadrilateral is a kite then it s diagonals are perpendicular.

Iam having a total mind blank right now.write a coordinate

bhopainting

09.01.2022

Theorem: If a quadrilateral is a kite then it's diagonals are perpendicular.

Proof:- In kite WXYZ, let O(a,b) be the intersection point of the diagonals .

Also the distance formula is given by ,

Distance from $(x_1,y_2)\ and\ (x_2,y_2)=\sqrt{(x_2-x_1)^2-(y_2-y_1)^2}$

In ΔWOX,

OX=a [since the coordinate of x changes but not y, thus the distance from O to X=a]

WO= 3b [since the coordinate of y changes but not x, thus the distance from O to W = 4b-b=3b]

WX= $\sqrt{(2a-a)^2+(4b-b)}=\sqrt{a^2+9b^2}$

We can see that

$WX^2=a^2+9b^2=OX^2+WO^2\\\Rightarrow\ WX^2=OX^2+WO^2$

$\\\Rightarrow\ \angle{WOX}=90^{\circ}$ [By the converse of Pythagoras theorem]

⇒ The diagonals are perpendicular.

Hence proved.

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lolh1520

09.05.2022

2/3

Step-by-step explanation:

Gradient = rise/run

rise = 80 - 60 = 20

run = 70 - 40 = 30

Gradient = 20/30 = 2/3

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