Practice Test


1) If the point (x,y) be equidistant from the points ( 6,-1) and (2,3), then x-y is equal to


2) The points P is equidistant from A ( 1,3), B(-3,5) and C(5,-1), then PA is equal to


3) Three vertices of a parallelogram taken in order are (-1, -6), ( 2,-5) and ( 7,2). The fourth vertex is


4) y-axis divides the segment joining points ( -3, -4 ) and (1,-2) in the ratio


5) Let AB be divided internally and externally at P and Q in the same ratio. Then, AP, AB and AQ are is


6) The straight lines x = y, x - 2y = 3 and x + 2y = -3 form a triangle, which is


7) Length of the median from B on AC, where A ( -1,3), B ( 1,-1), C ( 5,1) is


8) The centre of a circle which passes through points (1,1), (2,3) and (-2,2) is


9) Find the value of x for which the points (x, -1), (2,1) and (4,5) are collinear.


10) Area of quadrilateral whose vertices are (2,3), (3,4), (4,5) and (5,6), is equal to


11) If area of triangle with vertices (x,0), (1,1) and (0,2) is 4 sq units, then the value of x is


12) Let the opposite angular points of a square be (3,4) and (1,-1). Then, the coordinates of the remaining angular points are


13) If the vertices of a triangle have integral coordinates, the triangle cannot be


14) The x-coordinate of the incentre of the triangle where the mid-point of the sides are (0,1), (1,1) and (1,0), is


15) The orthocentre of the triangle formed by (0,0), (8,0) and (4,6) is


16) If orthocentre and circumcentre of triangle are respectively (1,1) and (3,2), then the coordinates of its centroid are


17) The incentre of the triangle formed by lines x = 0, y = 0 and 3x + 4y = 12, is at


18) The coordinates of the circumcentre of the triangle with vertices (8,6), (8,-2) and (2,-2) are


19) If two vertices of triangle are (-2,3) and ( 5, -1). Orthocentre lies at the origin and centroid on the line x + y = 7, then the third vertex lies at


20) If (0,1) is the orthocentre and (2,3) is the centroid of a triangle. Then, its circumcentre is


21) The centroid of a triangle is ( 2, 7 ) and two of its vertices are (4, 8) and (-2, 6). The third vertex is


22) the locus of a point P which moves such that 2 PA = 3 PB, where coordinates of points A and B are (0,0) and (4,-3), is


23) The locus of a point whose difference of distance from points (3,0) and (-3,0) is 4, is


24) What is the equation of the locus of a point which moves such that 4 times its distance from the x-axis is the square of its distance from the origin ?


25) A rod of length l sides with its ends on two perpendicular lines. The locus of a point which divides it in the ratio 1 : 2, is


26) A point moves in such a way that the sum of its distance from two fixed points (ae, 0) and (-ae, 0) is 2a. Then, the locus of the points is


27) A point moves is such a way that the sum of squares of its distance from A ( 2,0) and B ( -2,0 ) is always equal to the square of the distance between A and B, then the locus of point P is


28) If origin is shifted to ( 7,-4 ), then point ( 4,5 ) shifted to


29) A straight line with negative slope passing through the point ( 1, 4 ) meets the coordinate axes at A and B. The minimum value of OA + OB is equal to


30) A line L has intercepts a and b on the coordinate axes. Keeping the origin fixed, the axes are rotated through a fixed angle. Now, the same line has intercepts p and q on the new axes too many


31) The median BE and AD of a triangle with vertices A ( 0, b ), B ( 0, 0 ) and C ( a, 0) are perpendicular to each other, if


32) If the points (1,2) and (3,4) were to be on the same side of the line 3x - 5y + a =0, then


33) The points (1,3) and (5,1) are two opposite vertices of a rectangle. The other two vertices lie on the line y = 2x + c, are


34) Given points are A ( 0,4 ) and B ( 0,-4 ), the locus of P(x,y) such that | AP - BP| =6, is


35) The orthocentre of the triangle formed by the points (0,0), (4,0) and (3,4) is


36) The area of the region bounded by the lines y = | x-2 |, x = 1, x = 3 and the x-axis is


37) The middle point of the line segment joining (3,-1) and (1,1) is shifted by two units ( in the sense of increasing y ) perpendicular to the line segment. Then, the coordinates of the point in the new position are


38) ABC is an isosceles triangle, if the coordinates of the base are B ( 1,3) and C ( -2, 7), the coordinates of vertex A can be


39) The area of a triangle is 5 sq units. Two of its vertices are ( 2,1) and ( 3,-2). The third vertex lies on y = x+3. The coordinates of the third vertex can be


40) The point ( p+1, 1 ), (2p+1, 3 ) and ( 2p +2, 2p ) collinear, if


41) The coordinates of the point A and B are respectively ( -3,2 ) and ( 2,3 ). P and Q are points on the line joining A and B such that AP = PQ = QB. A square PQRS is constructed on PQ as one side, the coordinates of R can be


42) The sum of a + c is


43) Statement I If the circumcircle of a triangle lies at the origin and centroid is the middle point of the line joining the points ( 2, 3 ) and ( 4, 7 ), then its orthocentre lies on the line 5x - 3y = 0.
Statement II the circumcentre, centroid and the orthocentre of a triangle lies on the same line.


44) Statement I If sum of algebraic distances from points A (1,1), B (2,3), C ( 0,2) is zero on the line ax + by + c =0, then a + 3b + c = 0.
statement II The centroid of triangle is ( 1,2 ).


45) The x-coordinate of the incentre of the triangle that has the coordinates of mid - points of its sides as (0,0), (1,1) and (1,0) is


46) If the line 2x + y = k passes through the point which divides the line segment joining the points (1,1) and ( 2,4) in the ratio 3 : 2, then k is equal to


47) Let A ( h, k), B ( 1,1 ) and C ( 2,1 ) be the vertices of a right angled triangle with AC as its hypotenuse. If the area of the triangle is 1, then the set of values which k can take is given by


48) If a vertex of a triangle is (1,1) and the mid-point of two sides of a triangle through this vertex are (-1,2) and (3,2), then the centroid of the triangle is