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Alana is writing a coordinate proof to show that the diagonals of a rectangle are congruent. She starts by assigning coordinates to a rectangle as shown. Then she uses the coordinates to write and simplify expressions for the lengths of the diagonals.

Alana is writing a coordinate proof to show that the diagonals of a rectangle are congruent She starts by assigning coordinates to a rectangle as shown Then sh class=

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semsee45

Answer:

8.6

Step-by-step explanation:

Distance between two points

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]\textsf{where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points}.[/tex]

Define the points:

  • [tex]\textsf{Let}\:(x_1,y_1)=(0,0)[/tex]
  • [tex]\textsf{Let}\:(x_2,y_2)=(7,5)[/tex]

Substitute the defined points into the formula:

[tex]\implies d=\sqrt{(7-0)^2+(5-0)^2}[/tex]

[tex]\implies d=\sqrt{7^2+5^2}[/tex]

[tex]\implies d=\sqrt{49+25}[/tex]

[tex]\implies d=\sqrt{74}[/tex]

[tex]\implies d=8.6\;\;\sf (nearest\: tenth)[/tex]

Therefore, the length of one of the diagonals of the rectangle is 8.6.

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