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# 01%20-%20Point - Problems 01 POINT Page 1(1 Show that P a b...

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Problems 01 - POINT Page 1 ( 1 ) Show that P ( a, b + c ), Q ( b, c + a ) and R ( c, a + b ) are collinear. ( 2 ) Prove that the two lines joining the mid-points of the pairs of opposite sides and the line joining the mid-points of the diagonals of a quadrilateral are concurrent. ( 3 ) If ( 2, 3 ), ( 4, 5 ) and ( a, 2 ) are the vertices of a right triangle, find a. [ Ans: 3, 7 ] ( 4 ) Find the circumcentre of the triangle with vertices ( - 1, 1 ), ( 0, - 4 ) and ( - 1, - 5 ) and deduce that the circumcentre of the triangle whose vertices are ( 2, 3 ), ( 3, - 2 ) and ( 2, - 3 ) is the origin. [ Ans: ( - 3, - 2 ) ] ( 5 ) For which value of a would the area of a triangle with vertices ( 5, a ), ( 2, 5 ) and ( 2, 3 ) be 3 units ? [ Ans: For any a R ] ( 6 ) Find the area of the triangle whose vertices are ( l 2 , 2 l ), ( m 2 , 2 m ) and (n 2 , 2 n ) if l m n. [ Ans: l ( l - m ) ( m - n ) ( n - l ) l ] ( 7 ) Find the area of the triangle whose vertices are ( 5, 3 ), ( 4, 5 ) and ( 3, 1 ) and show that the triangle whose vertices are ( - 2, 2 ), ( - 3, 4 ) and ( - 4, 0 ) has the same area. [ Ans: 3 units ] ( 8 ) Find the area of the triangle with vertices ( 5, 3 ), ( 4, 5 ) and ( 3, 1 ) by shifting the origin at ( 5, 3 ). [ Ans: 3 units ] ( 9 ) Prove that the mid-point of the segment joining the two points dividing AB from A in the ratios m : n and n : m is the mid-point of AB .

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Problems 01 - POINT Page 2 ( 10 ) If P ( 1, 2 ) and Q ( 5, 6 ) divide AB from A in the ratios 2 : 1 and - 2 : 1, find the co-ordinates of A and B. [ Ans: A ( - 1, 0 ), B ( 2, 3 ) ] ( 11) If ( 3, 2 ), ( 4, 5 ) and ( 2, 3 ) are three of the four vertices of a parallelogram, find the co-ordinates of the fourth vertex. [ Ans: ( 5, 4 ), ( 3, 6 ), ( 1, 0 ) ] ( 12 ) Show that the points ( 2, 3 ), ( 4, 5 ) and ( 3, 2 ) can be the vertices of a rectangle and find the co-ordinates of the fourth vertex.
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01%20-%20Point - Problems 01 POINT Page 1(1 Show that P a b...

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