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the cordinates of the feet of perpendiculars from the vertices of a triangle on the opposite sides are (20,25), (8,16), (8,9) so the coordinates of a vertexof the triangle are

the cordinates of the feet of perpendiculars from the vertices of a triangle on the opposite sides are (20,25), (8,16), (8,9) so the coordinates of a vertexof the triangle are

Grade:11

1 Answers

Mayank
368 Points
3 years ago
 
we take a triangle ABC and draw 3 perpendiculars from the three vertices we get AL ,BM,CN
now we have a concept that the triange formed by the points LMN is a pedal triangle and the orthocentre of ABC triangle =the incentre of triangle LMN so finding the incentre of triangle LMN we get the point (10,15) which is also the orthocentre of tringle ABC
note: for the incentre i used the formulae  (lx1 + mx2 + nx3)/l+m+n and similarly for the y coordinate
now slope of AL is -1/2 and as AL is perpendicular to BC so slope of BC is 2 similarly for other two sides we get the slope of AB=-1/3  and slope of AC is -1 so now using these points we have
equation of AB ---------->   3y+x=35
equation of AC ---------->  x+y=45
equation of BC ---------->  y=2x
now AB equation satisfies option A,B
AC equation satisfies option B,C
BC equation satisfies option A,C

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