State True or False that (0,5),(-2,-2),(5,0),(7,7)are the vertices of a rhombus. - Sri Chaitanya Infinity Learn Best Online Courses for NCERT Solutions, CBSE, ICSE, JEE, NEET, Olympiad and Class 6 to 12

A
True
B
False

Solution:

Let us consider

A (0, 5), B (- 2, - 2), C (5, 0) and D (7, 7)

as the vertices of the quadrilateral.
As we know that the length of all sides of a rhombus are equal whereas the length of the diagonal of the rhombus are not equal.
So, to prove that A,B,C and D are the vertices of a rhombus it is necessary to find the length of its sides and diagonals.
The length of line that joins two points

(x 1 y 1) and (x 2 y 2) =

\sqrt{{(x 1 - x 2)}^{2} + {(y 1 - y 2)}^{2}}

Length of the side AB =

\sqrt{{(0 - (- 2))}^{2} + {(5 - (- 2))}^{2} =} \sqrt{53}

Length of the side BC=

\sqrt{{(- 2 - 5)}^{2} + {(- 2 - 0)}^{2}}

=

\sqrt{53}

Length of the side CD =

\sqrt{{(5 - 7)}^{2} + {(0 - 7)}^{2}} = \sqrt{53}

Length of the side AD=

\sqrt{{(7 - 0)}^{2} + {(7 - 5)}^{2}} = \sqrt{53}

Length of the side AC =

\sqrt{{(0 - 5)}^{2} + {(5 - 0)}^{2}} = \sqrt{50}

Length of the side BD =

\sqrt{{(- 2 - 7)}^{2} + {(- 2 - 7)}^{2}} = \sqrt{162}

Therefore, (0 , 5), (- 2,- 2), (5,0) and (7,7) are the vertices of a rhombus as the length of each side of the rhombus is equal and it has unequal diagonals.

State True or False that $(0, 5), (- 2, - 2), (5, 0), (7, 7)$ are the vertices of a rhombus.

Solution:

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