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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Answer:
Refer to the diagram above.
First of all join AC.
Then, find the distance between
1) A and C = (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 = = 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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