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Q.

In a triangle PQR, the co-ordinates of the points P and Q are (-2,4) and (4,-2) respectively. If the equation of perpendicular bisector of PR is 2x-y+2=0, then the centre of the circumcircle of the ΔPOR is

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a

−2,−2

b

0,2

c

1,4

d

−1,0

answer is A.

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Detailed Solution

Since the circum center is at equal distances from all the vertices. SP=SQ⇒x+22y−422=x−42+y+22⇒4x+4−8y+16=−8x+16+4y+4⇒12x=12y⇒x=y And the circum center lies on the line line 2x-y+2=0 Hence, x=-2 and y=-2

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