A rhombus, which is a quadrilateral with 4 equal sides, is plotted on the coordinate plane. The coordinates of the vertices are (2, 0), (7, 0), (5, 4), and (10, 4). How long is each side of the rhombus?.

The slanted sides are each the hypotenuse of a 3-4-5 right triangle, so are also 5 units long. (You expect all of the sides of the rhombus to be the same length.)

Each side is 5 units long.

TNpriyangi TNpriyangi · Answer 2 · 2022-12-23T18:28:10-05:00

The answer is 5, 4.47, 5, and 8.94.

Step 1: Determine the length of the sides using the distance formula.

The distance formula is d = √(x2-x1)^2 + (y2-y1)^2

Step 2: Calculate the length of the first side. To do this, plug in the coordinates for the two points that make up the first side into the distance formula. This side is formed by the points (2, 0) and (7, 0).

d = √(7-2)^2 + (0-0)^2

d = √(5)^2 + (0)^2

d = √(25) + (0)

d = 5

Step 3: Calculate the length of the second side. To do this, plug in the coordinates for the two points that make up the second side into the distance formula. This side is formed by the points (7, 0) and (5, 4).

d = √(5 - 7)^2 + (4 - 0)^2

d = √(-2)^2 + (4)^2

d = √4 + 16

d = √20

d = 4.47

Step 4: Calculate the length of the third side. To do this, plug in the coordinates for the two points that make up the third side into the distance formula. This side is formed by points (5, 4) and (10, 4).

d = √(10 - 5)^2 + (4 - 4)^2

d = √25 + 0

d = 5

Step 5: Calculate the length of the fourth side. To do this, plug in the coordinates for the two points that make up the fourth side into the distance formula. This side is formed by the points (10, 4) and (2, 0).

d = √(2 - 10)^2 + (0- 4)^2

d = √(-8)^2 + (-4)^2

d = √64 + 16

d = √80

d = 8.94

Therefore, each side of the rhombus has a length of 5, 4.47, 5, and 8.94.

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