Bunuel wrote:
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 4 units
(1) The distance between the point C and point B(1, 5) is 2units
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 = 4 units.
Hence, the statements individually are not sufficient and we can eliminate A, B, andD.
Combined
From statement 1 we know
\( (x-5)^2 + (y-5)^2 =4^2\) -- Eq(1)
From statement 2 we know
\( (x-1)^2 + (y-5)^2 =2^2\) -- Eq(2)
Eq(1) -Eq(2)
\( (x-5)^2 - (x-1)^2 = 4^2-2^2\)
\( (x-5+x-1)(x-5-x+1) =(4+2)(4-2)\)
\( (2x-6)(-4) =6*2\)
\( (2x-6) =-3\)
\( x =\frac{3}{2}\)
y =
\( (x-1)^2 + (y-5)^2 =2^2\)
\((\frac{3}{2} -1)^2 + (y-5)^2 =2^2\)
\( (y-5)^2 = 4 -\frac{1}{4}\)
\( (y-5)^2 = 3.75\)
\( y = 5 \pm\sqrt{3.75} \)
We can have two pairs of (x,y), therefore, the statements
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Statistics : Posted by gmatophobia • on 25 Jun 2023, 01:32 • Replies 1 • Views 159
