Prove that the diagonals of kite uvwx are perpendicular.

step 1: determine the slope of xv.

the slope of xv is .

step 2: determine the slope of uw.

the slope of uw is .

step 3: the slopes of the diagonals are .

the diagonals of kite uvwx are

Answer with explanation:

Given: A kite U V W X

To Prove: Diagonals of kite U V W X, that is ,U W and V X are Perpendicular.

Proof:

Slope between two points having position vector or coordinates , is given by:

               

Step 1:

Determine the slope of XV. Suppose position vector of point X is (a,b) and Position vector of point V is (p,q).

The slope of XV is

       

Step 2:

Determine the slope of UW. Suppose position vector of point U is (m,n) and Position vector of point W is (s,t).

The slope of U W is :

 

Step 3: The slopes of the diagonals are,

Also,

→→Showing that,The diagonals of kite UVWX are perpendicular to each other.

 

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