Q.

If the ends of the base of an isosceles triangle are at (2,0) and (0,1) and the equation of one side is x=2  then the orthocenter of the triangle is

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a

(3/2,3/2)

b

(5/4,1)

c

(3/4,1)

d

(4/3,7/12)

answer is B.

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Detailed Solution

Form the figure,22+(y1−1)2=y12 4+y12+1−2y1=y12 5=2y1  or   y1=5/2 Equation of the line form (2,5/2) to the given base isy−5/2=2(x−2) or 2y−5=4(x−2) At y=1 , −3/4=x−2 Or x=5/4
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If the ends of the base of an isosceles triangle are at (2,0) and (0,1) and the equation of one side is x=2  then the orthocenter of the triangle is