Complete the coordinate proof of the theorem. Given: ABCD is a rectangle.
Prove: The diagonals of ABCD are congruent.

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The coordinates of rectangle ABCD are A(0, 0), B(, 0) , C(a, b), and D(0, ) .

The length of AC⎯⎯⎯⎯⎯ is equal to .

The length of BD⎯⎯⎯⎯⎯ is equal to .

The diagonals of the rectangle have the same length.

Therefore, the diagonals of ABCD are congruent.

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

answer: the equation matches the regression

step-by-step explanation:

1 x=22.52

2: 65/39=604+39x

65x-39x=604

26x=604

x=604/26

×=23.23

h/o/e/s mad

step-by-step explanation:

si si si