Martin wants to use coordinate geometry to prove that the opposite sides of a rectangle are congruent. He places parallelogram ABCD in the coordinate plane so that A is (0, 0), B is (a, 0), C is (a, b), and D is (0, b).

What formula can he use to determine the distance from point D to point A?

A.(0-0)^2+(b-0)^2=b^2
B.(a-a)^2+(b-0)=b^2
C.sqaure root of (a-a)^2+(b-0)^2=square root of b^2=b
D.square root of (0-0)^2+(b-0)^2=square root of b^2=b

The answer is D(square root of (0-0)^2+(b-0)^2=square root of b^2=b) just took a quiz with the same question.

die

This answer does not help in anyway, just answer the question

To determine the distance between two points, Martin can use the distance formula, which is derived from the Pythagorean theorem.

The distance formula is given by:

d = √((x2 - x1)^2 + (y2 - y1)^2)

In this case, point D is (0, b) and point A is (0, 0). So, Martin can substitute the values into the distance formula:

d = √((0 - 0)^2 + (b - 0)^2)

Simplifying this expression gives:

d = √(0 + b^2)

This further simplifies to:

d = √(b^2)

And since the square root of b^2 is b, the correct answer is:

D. √(0 - 0)^2 + (b - 0)^2 = √(b^2) = b

Martin wants to use coordinate geometry to prove that the opposite sides of a rectangle are congruent. He places parallelogram ABCD in the coordinate plane so that A is (0, 0), B is (a, 0), C is (a, b), and D is (0, b).

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A(0,0), B(a,0). AB is a hor. line, because Y is constant.

AB = a - 0 = a.

D(0,b), C(a,b). DC is a hor. line.
DC = a - 0 = a.

AB = DC, Because quantities that are =
to the same or = quantities are = to
each other.

A(0,0), D(0,b). AD is a Vertical line,
because X is constant.
AD = b - 0 = b.

B(a,0), C(a,b). BC is a vertical line,
because X is constant.
BC = b - 0 = b.

AD = BC, Because quantities that are =
to the same or = quantities are = to
each other.

(0,0)2