Show that the points (7,3) (3,0) …

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Show that the points (7,3) (3,0) (0,-4) (4,-1)are vertices of rhombus

Posted by Kanishk Goyal 7 years, 3 months ago

CBSE > Class 10 > Mathematics

1 answers

Shweta Gulati 7 years, 3 months ago

Let A(7,3) , B(3,0) , C(0,-4) and D(4,-1) represent the points.

To prove that these points are vertices of a rhombus we have to show that all sides are equal. We may calculate it using distance formula.

AB= $\sqrt{(3 - 7)^{2} + (0 - 3)^{2}} = \sqrt{16 + 9} = \sqrt{25} = 5 u n i t s$

BC= $\sqrt{(0 - 3)^{2} + (- 4 - 0)^{2}} = \sqrt{9 + 16} = \sqrt{25} = 5 u n i t s$

CD= $\sqrt{(4 - 0)^{2} + (- 1 + 4)^{2}} = \sqrt{16 + 9} = \sqrt{25} = 5 u n i t s$

DA= $\sqrt{(7 - 4)^{2} + (3 + 1)^{2}} = \sqrt{9 + 16} = \sqrt{25} = 5 u n i t s$

The diagonals are not equal.

AC= $\sqrt{(7 - 0)^{2} + (3 + 4)^{2}} = \sqrt{49 + 49} = \sqrt{98} = 7 \sqrt{2} u n i t s$

BD= $\sqrt{(4 - 3)^{2} + (- 1 - 0)^{2}} = \sqrt{1 + 1} = \sqrt{2} u n i t s$

This shows that these points are vertices of rhombus.

2Thank You

ANSWER

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