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Question

In the coordinate plane, the points F(2,1),G(1,4) and H(4,1) lie on a circle with center P. What are the coordinates of point P ?

A
(0,0)
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B
(1,1)
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C
(1,2)
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D
(1,2)
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Solution

The correct option is B (1,1)
Let H(x1,y1)=(4,1)
G(x2,y2)=(1,4)
F(x3,y3)=(2,1)
P(x,y)
slope of mr=y2y1x2x1=4114=1
slope of mt=y3y2x3x2=1421=1
Formula for x-coordinate of the center of the circle is given as:
x=mrmt(y3y1)+mr(x2+x3)mt(x1+x2)2(mrmt)
x=(1)(1)(11)+1(1+(2))1(4+1)2(11)
x=0+154=1
y=1mr[xx1+x22]+y1+y22
y=11[14+12]+1+42
y=[252]+52=1
P(1,1)
Hence, option B is correct.

599035_498228_ans_e5b85a704a684154812039d3d7ce6e28.png

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