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State whether the given statement is true or false.

The rhombus-shaped quadrilateral has vertices (1,3), (2,6), (5,7), and (4,4).

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True

False

answer is A.

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Detailed Solution

We have been given,
The rhombus-shaped quadrilateral has vertices (1,3), (2,6), (5,7), and (4,4).
Using the distance formula,

D = x 2 − x 1 2 + y 2 − y 1 2

Calculating the distance between the points,
For AB, substituting

x_{2} = 2, x_{1} = 1, y_{2} = 6, and y_{1} = 3

, in the formula,

AB = \sqrt{{(2 - 1)}^{2} + {(6 - 3)}^{2}}

For BC, substituting

x_{2} = 5, x_{1} = 2, y_{2} = 7, and y_{1} = 6

, in the formula,

BC = \sqrt{{(5 - 2)}^{2} + {(7 - 6)}^{2}}

For CD, substituting

x_{2} = 5, x_{1} = 4, y_{2} = 7, and y_{1} = 4

, in the formula,

CD = \sqrt{{(5 - 4)}^{2} + {(7 - 4)}^{2}}

For AD, substituting

x_{2} = 4, x_{1} = 1, y_{2} = 4, and y_{1} = 3

, in the formula,

AD = \sqrt{{(4 - 1)}^{2} + {(4 - 3)}^{2}}

Also, calculating the length of the diagonals,
For AC, substituting

x_{2} = 5, x_{1} = 1, y_{2} = 7, and y_{1} = 3

, in the formula,

AC = \sqrt{{(5 - 1)}^{2} + {(7 - 3)}^{2}}

For BD, substituting

x_{2} = 4, x_{1} = 2, y_{2} = 6, and y_{1} = 4

, in the formula,

BD = \sqrt{{(4 - 2)}^{2} + {(6 - 4)}^{2}}

As the rhombus's sides are the same length but the lengths of the diagonals are not equal, thus it is a rhombus.
Therefore, our statement is true.
Hence, option 1 is correct.

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State whether the given statement is true or false.The rhombus-shaped quadrilateral has vertices (1,3), (2,6), (5,7), and (4,4).

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State whether the given statement is true or false.

The rhombus-shaped quadrilateral has vertices (1,3), (2,6), (5,7), and (4,4).