Question

andi is proving that a quadrilateral ( f(-2,1) ), ( g(0,-3) ), ( h(6,0) ), ( i(4,4) ) is a rectangle. she states that the diagonals are congruent. to prove th are the lengths of the diagonals?

a ( 45 )
b do not select this choice
c ( sqrt{65} )
d ( sqrt{45} )
e ( 65 )

Explanation:

Step1: Use the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
For diagonal \(FH\) with \(F(-2,1)\) and \(H(6,0)\):

$$
LATEXBLOCK0
$$

Step2: Calculate the other diagonal

For diagonal \(GI\) with \(G(0,-3)\) and \(I(4,4)\):

$$
LATEXBLOCK1
$$

Answer:

C. \(\sqrt{65}\)