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04 Aug 2021, 07:45
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24% (01:40) correct
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In the right coordinate plane, the distance between the point (0, 0) and the point P is 10. What are the coordinates of point P?
(1) The distance between (16, 0) and P is 10.
(2) The distance between (12, 16) and P is 10.
(1) The distance between (16, 0) and P is 10.
(2) The distance between (12, 16) and P is 10.
05 Aug 2021, 20:39
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sjuniv32
The question is a very simple one, if you can realise and convert each statement into a circle. No formulas required, no intensive calculations required, just visualisation.
We can say that P lies on a circle that has its Center at the origin (0,0) and has a radius of 10.
Now the two statements also give a circle that has a origin somewhere else, but contains P on its circumference.
If the statement gives a circle that will intersect the original circle at two points, then two positions of P possible, but if they intersect at just one point, then the point is P.
1) The distance between (16, 0) and P is 10.
The question is how to know that the circles intersect at two points and that too quickly.
Distance between the centres of the two circles with origin (0,0) and (16,0) is \(\sqrt{(16-0)^2+(0-0)^2}=16\).
But distance of P is 10 from each origin, so surely the two circles intersect at two points.
Insufficient
2) The distance between (12, 16) and P is 10.
Distance between the centres of the two circles with origin (0,0) and (12,16) is \(\sqrt{(16-0)^2+(12-0)^2}=\sqrt{16^2+12^2}=\sqrt{400}=20\).
But distance of P is 10 from each origin, so P is exactly at the Center of the line joining two circles.
Thus two intersect at just one point, which is P.
Sufficient
B
30 Oct 2023, 23:02
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