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Mathematics

AOBC is a rectangle whose three vertices are A(0, 3), O(0, 0) and B(5, 0). The length of its diagonal is

  1. 5 units

  2. 3 units

  3. 34\sqrt{34} units

  4. 4 units

Coordinate Geometry

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Answer

Since, AOBC is the rectangle.

So, AB will be the diagonal.

AOBC is a rectangle whose three vertices are A(0, 3), O(0, 0) and B(5, 0). The length of its diagonal is? Coordinate Geometry, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

By distance formula,

d=(x2−x1)2+(y2−y1)2∴AB=(5−0)2+(0−3)2=(5)2+(−3)2=25+9=34 units.d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2} \\[1em] \therefore AB = \sqrt{(5 - 0)^2 + (0 - 3)^2} \\[1em] = \sqrt{(5)^2 + (-3)^2} \\[1em] = \sqrt{25 + 9} \\[1em] = \sqrt{34} \text{ units}.

Hence, Option 3 is the correct option.

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