Find the coordinate point for D that would make ABDC a rhombus.

coordinate plane with points A 2 comma 2, B 3 comma 4, and C 4 comma 1

(5, 4)
(5, 2)
(5, 3)
(3, 0)

Answers

Answer 1

Answer: The correct answer is (5, 3)

Step-by-step explanation: I got it right on the exam

Answer 2

(5,3) will make a rhombus.

What is Rhombus?

A Quadrilateral with all sides equal but with nonequal diagonals is know as Rhombus.

How to solve?

Let D have coordinate (x,y)

The length of all the sides of the rhombus is equal.

length of AB = [tex]\sqrt{({2-3})^2 + ({2-4})^2} = \sqrt{1+4} = \sqrt{5}[/tex]

Similarly BD = [tex]\sqrt{({3-x})^2 + ({4-y})^2} = \sqrt{25+{x}^2+{y}^2-6x-8y}[/tex] -------------(1)

CD = [tex]\sqrt{({4-x})^2 + ({1-y})^2} = \sqrt{17+{x}^2+{y}^2-8x-2y}[/tex] -------------(2)

We know BD = CD gives,

[tex]\sqrt{17+{x}^2+{y}^2-8x-2y} = \sqrt{25+{x}^2+{y}^2-6x-8y}[/tex]

By squaring both sides and solving we get,

3y - x = 4 ----------------------(3)

Since BCD is a right-angled triangle,

[tex]{BC}^2 = {BD}^2 + {CD}^2[/tex]  

BC = [tex]\sqrt{10}[/tex]

10 = 5 + [tex]\sqrt{17+{x}^2+{y}^2-8x-2y}[/tex]

8  = [tex]{x}^2+{y}^2-8x-2y[/tex] -------------------(4)

solving equation (3) and (4) we get x = 5 and y = 3

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You will need
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Answer:

Step-by-step explanation:

The number 4/9 is a rational number. It is a ratio, or fraction, made up of two integers, 4 and 9. So a rational number less than 4/9 will be any fraction less.

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

Answer:

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Answers

Answer:

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Answer:

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Answer/Step-by-step explanation:

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Answers

Answer:

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you can chose to belive me or not

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To learn more about the right-angled triangle;

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