Math, asked by prathanakarki145, 5 months ago

If A(3, 4),B (3,-3) and C ( 6, - 3) are the points, prove that AB and BC are proportional.

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Answers

Answered by Arbaazhussainckpatif
1

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Answered by sukhdeepkhera0127
22

Answer:

Refer to the diagram above.

First of all join AC.

Then, find the distance between

1) A and C =  \sqrt{58} (second picture)

2) B and C = 3 (third picture)

3) A and B = 7 (fourth picture)

Now, according to the pythagoras theorem,

Base² + Perpendicular² = Hypotenuse²

AC is the longest side. So if

BC² + AB² = AC² then it will be proved that AB and BC are proportional.

BC² + AB² = 3² + 7² = 9 + 49 = 58

AC² =  \sqrt{58 {}^{2} } = 58

Hence AC² = BC² + AB²

Pythagoras theorem is proved.

So the angle opposite to hypotenuse will be perpendicular.

Thus, AB and BC are perpendicular.

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