हिंदी

The Points a (2, 0), B (9, 1), C (11, 6) and D (4, 4) Are the Vertices of a Quadrilateral Abcd. Determine Whether Abcd is a Rhombus Or Not.

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प्रश्न

The points A (2, 0), B (9, 1), C (11, 6) and D (4, 4) are the vertices of a quadrilateral ABCD. Determine whether ABCD is a rhombus or not.

योग
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उत्तर

The given points are A (2, 0), B (9, 1), C (11, 6) and D (4, 4).
Let us find the length of all the sides of the quadrilateral ABCD.

\[AB = \sqrt{\left( 2 - 9 \right)^2 + \left( 0 - 1 \right)^2} = \sqrt{50} = 5\sqrt{2}\]
\[BC = \sqrt{\left( 11 - 9 \right)^2 + \left( 6 - 1 \right)^2} = \sqrt{29}\]
\[CD = \sqrt{\left( 4 - 11 \right)^2 + \left( 4 - 6 \right)^2} = \sqrt{49 + 4} = \sqrt{53}\]
\[AD = \sqrt{\left( 4 - 2 \right)^2 + \left( 4 - 0 \right)^2} = \sqrt{4 + 16} = 2\sqrt{5}\]
\[\because AB \neq BC \neq CD \neq AD\], quadrilateral ABCD is not a rhombus.
shaalaa.com
Brief Review of Cartesian System of Rectanglar Co-ordinates
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 22: Brief review of cartesian system of rectangular co-ordinates - Exercise 22.1 [पृष्ठ १३]

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आर.डी. शर्मा Mathematics [English] Class 11
अध्याय 22 Brief review of cartesian system of rectangular co-ordinates
Exercise 22.1 | Q 4 | पृष्ठ १३

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