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25 Jun 2023, 01:32
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C
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Difficulty:
35%
(medium)
Question Stats:
71% (01:12) correct
29%
(00:53)
wrong
based on 31
sessions
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In a rectangular coordinate system, what are the coordinates of point C?
(1) The distance between the point C and point A(5, 5) is 2 units
(1) The distance between the point C and point B(1, 5) is 2 units
(1) The distance between the point C and point A(5, 5) is 2 units
(1) The distance between the point C and point B(1, 5) is 2 units
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25 Jun 2023, 11:44
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Bunuel
Statements 1 and Statement 2 are individually not sufficient. As C can be any point on the circumference of the circle with the given coordinates and radius.
For example, in statement 1, C can be a point on the circumference of the circle with the center at (5,5) and radius = 2 units.
Hence, the statements individually are not sufficient and we can eliminate A, B, and D.
Combined
From statement 1 we know
\((x-5)^2 + (y-5)^2 = 2^2\) -- Eq(1)
From statement 2 we know
\((x-1)^2 + (y-5)^2 = 2^2\)-- Eq(2)
Eq(1) - Eq(2)
\((x-5)^2 - (x-1)^2 = 2^2 -2^2\)
\((x-5+x-1)(x-5-x+1) = 0\)
\((2x-6)(-4) = 0\)
\((2x-6) = 0\)
\(x = 3\)
y =
\((3-1)^2 + (y-5)^2 = 2^2\)
\((y-5)^2 = 0\)
\(y = 5\)
As we have a unique pair of values for (x,y), the statements combined are sufficient to arrive at the value of point C.
Option C
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