Question

Prove that the diagonals of kite UVWX are perpendicular.

Answer 1

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 ,$A(x_{1},y_{1}) {\text{and}} B(x_{2},y_{2})$ is given by:

               $=\frac{\text{Difference in y coordinates}}{\text{Difference in x coordinates}}\\\\=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

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

        $m_{1}=\frac{q-b}{p-a}$

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 :

 $m_{2}=\frac{t-n}{s-m}$

Step 3: The slopes of the diagonals are, $m_{1},m_{2}$

Also, $m_{1}\times m_{2}=-1$

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

 

Answer 2

Answer:

1, -1, negative reciprocals, perpendicular

Step-by-step explanation: