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Home » State whether the following statements are true or false. Justify your answer. Points A (4, 3), B (6, 4), C (5, –6) and D (–3, 5) are the vertices of a parallelogram.
State whether the following statements are true or false. Justify your answer. Points A (4, 3), B (6, 4), C (5, –6) and D (–3, 5) are the vertices of a parallelogram.
CBSE | Class 10 | Coordinate Geometry | Exercise 7.2 | Maths | NCERT Exemplar
State whether the following statements are true or false. Justify your answer. Points A (4, 3), B (6, 4), C (5, –6) and D (–3, 5) are the vertices of a parallelogram.

Solution:

The statement given in the question is false.

Justification:

A (4, 3), B (6, 4), C (5, –6) and D (–3, 5) are the points given.

We need to find the distance between A and B

AB=\sqrt{{{\left( 6-4 \right)}^{2}}+{{\left( 4-3 \right)}^{2}}}=\sqrt{{{2}^{2}}+{{1}^{2}}}=\sqrt{5}

Now, find the distance between B and C.

BC=\sqrt{{{\left( 5-6 \right)}^{2}}+{{\left( -6-4 \right)}^{2}}}

BC=\sqrt{{{\left( -1 \right)}^{2}}+{{\left( -10 \right)}^{2}}}

BC=\sqrt{1+100}=\sqrt{101}

Now, find the distance between C and D

CD=\sqrt{{{\left( -3-5 \right)}^{2}}+{{\left( 5+6 \right)}^{2}}}

CD=\sqrt{{{\left( -8 \right)}^{2}}+{{\left( 11 \right)}^{2}}}

CD=\sqrt{64+121}=\sqrt{185}

Now, find the distance between D and A

DA=\sqrt{{{\left( 4+3 \right)}^{2}}+{{\left( 3-5 \right)}^{2}}}

DA=\sqrt{{{7}^{2}}+{{\left( -2 \right)}^{2}}}

DA=\sqrt{49+4}=\sqrt{53}

We may conclude that the points are not vertices of a parallelogram because the distances are different.

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