On a coordinate plane, kite U V W X with diagonals is shown. Point U is at (negative 2, 5), point V is at (5, 4), point W is at (8, negative 5), and point X is at (negative 1, negative 2). 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
.

option 1 is correct.

step-by-step explanation:

y varies inversely with x and constant of variation is 4

the equation will be:

y = k/x

where k =4 so,

y = 4/x

if we put values of x of option 1 in the above equation and find values of y

y = 4/-2 => y =-2

y = 4/-1 => y = -4

y = 4/1 => y = 4

y = 4/2 => y =2

so, all the values of x and y are correct.

if we put values of x given in other options and find value of y we cannot find whole table satisfying the equation.

hence option 1 is correct.