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Without Distance Formula, Show that the Points A(5,8), B(4,4), C(0,5) and D(1,9) Form a Rhombus. - Mathematics

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प्रश्न

Without distance formula, show that the points A (5,8), B (4,4), C (0,5) and D (1,9) form a rhombus.
योग

उत्तर

We have to prove that ABCD is a rhombus

Slope of AC = `("y"_2 - "y"_1)/("x"_2 - "x"_1) = (5 - 8)/(0 - 5) = (-3)/(-5) = 3/5`

Slope of BD = `("y"_2 - "y"_1)/("x"_2 - "x"_1) = (9- 4)/(1 - 4)  = 5/(-3)`

Thus,Slope of AC x slope of BD = -1

So, the diagnols AC and BC are perpendicular to each other.

Hence,ABCD is a rhombus.

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अध्याय 13: Equation of A Straight Line - Exercise 13.2

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फ्रैंक Mathematics - Part 2 [English] Class 10 ICSE
अध्याय 13 Equation of A Straight Line
Exercise 13.2 | Q 19

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