(1) PQRS is a rectangle formed by joining the points P(-1,-1), Q(-1, 4), R(5, 4) and S(5,-1) . A, B, C and D are the mid-points of PQ, QR, RS and SP respectively. Is the quadrilateral ABCD a square, a rectangle or a rhombus? Justify your answer. Solution
(2) The area of a triangle is 5 sq.units. Two of its vertices are (2, 1) and (3, –2). The third vertex is (x, y) where y = x + 3 . Find the coordinates of the third vertex.
(3) Find the area of a triangle formed by the lines 3x + y − 2 = 0 , 5x + 2y − 3 = 0 and 2x − y − 3 = 0 Solution
(4) If vertices of quadrilateral are at A(-5, 7) , B(-4, k) , C(-1, -6) and D(4, 5) and its area is 72 sq.units. Find the value of k. Solution
(5) Without using distance formula, show that points (-2, -1) , (4, 0) , (3, 3) and (-3, 2) are the vertices of a parallelogram. Solution
(6) Find the equations of the lines, whose sum and product of intercepts are 1 and –6 respectively. Solution
(7) The owner of a milk store finds that, he can sell 980 litres of milk each week at ₹14/litre and 1220 litres of milk each week at ₹16/litre. Assuming a linear relationship between selling price and demand, how many litres could he sell weekly at ₹17/litre? Solution
(8) Find the image of the point (3,8) with respect to the line x + 3y = 7 assuming the line to be a plane mirror Solution
(9) Find the equation of a line passing through the point of intersection of the lines 4x + 7y − 3 = 0 and 2x − 3y + 1 = 0 that has equal intercepts on the axes. Solution
(10) A person standing at a junction (crossing) of two straight paths represented by the equations 2x −3y + 4 = 0 and 3x + 4y −5 = 0 seek to reach the path whose equation is 6x −7y + 8 = 0 in the least time. Find the equation of the path that he should follow. Solution
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