# Practice Test

Q1) If the point (x,y) be equidistant from the points ( 6,-1) and (2,3), then x-y is equal to Show Answer

Q2) The points P is equidistant from A ( 1,3), B(-3,5) and C(5,-1), then PA is equal to Show Answer

Q3) Three vertices of a parallelogram taken in order are (-1, -6), ( 2,-5) and ( 7,2). The fourth vertex is Show Answer

Q4) y-axis divides the segment joining points ( -3, -4 ) and (1,-2) in the ratio Show Answer

Q5) Let AB be divided internally and externally at P and Q in the same ratio. Then, AP, AB and AQ are is Show Answer

Q6) The straight lines x = y, x - 2y = 3 and x + 2y = -3 form a triangle, which is Show Answer

Q7) Length of the median from B on AC, where A ( -1,3), B ( 1,-1), C ( 5,1) is Show Answer

Q8) The centre of a circle which passes through points (1,1), (2,3) and (-2,2) is Show Answer

Q9) Find the value of x for which the points (x, -1), (2,1) and (4,5) are collinear. Show Answer

Q10) Area of quadrilateral whose vertices are (2,3), (3,4), (4,5) and (5,6), is equal to Show Answer

Q11) If area of triangle with vertices (x,0), (1,1) and (0,2) is 4 sq units, then the value of x is Show Answer

Q12) Let the opposite angular points of a square be (3,4) and (1,-1). Then, the coordinates of the remaining angular points are Show Answer

Q13) If the vertices of a triangle have integral coordinates, the triangle cannot be Show Answer

Q14) 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 Show Answer

Q15) The orthocentre of the triangle formed by (0,0), (8,0) and (4,6) is Show Answer

Q16) If orthocentre and circumcentre of triangle are respectively (1,1) and (3,2), then the coordinates of its centroid are Show Answer

Q17) The incentre of the triangle formed by lines x = 0, y = 0 and 3x + 4y = 12, is at Show Answer

Q18) The coordinates of the circumcentre of the triangle with vertices (8,6), (8,-2) and (2,-2) are Show Answer

Q19) 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 Show Answer

Q20) If (0,1) is the orthocentre and (2,3) is the centroid of a triangle. Then, its circumcentre is Show Answer

Q21) The centroid of a triangle is ( 2, 7 ) and two of its vertices are (4, 8) and (-2, 6). The third vertex is Show Answer

Q22) 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 Show Answer

Q23) The locus of a point whose difference of distance from points (3,0) and (-3,0) is 4, is Show Answer

Q24) 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 ? Show Answer

Q25) 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 Show Answer

Q26) 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 Show Answer

Q27) 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 Show Answer

Q28) If origin is shifted to ( 7,-4 ), then point ( 4,5 ) shifted to Show Answer

Q29) 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 Show Answer

Q30) 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 Show Answer

Q31) 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 Show Answer

Q32) If the points (1,2) and (3,4) were to be on the same side of the line 3x - 5y + a =0, then Show Answer

Q33) 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 Show Answer

Q34) Given points are A ( 0,4 ) and B ( 0,-4 ), the locus of P(x,y) such that | AP - BP| =6, is Show Answer

Q35) The orthocentre of the triangle formed by the points (0,0), (4,0) and (3,4) is Show Answer

Q36) The area of the region bounded by the lines y = | x-2 |, x = 1, x = 3 and the x-axis is Show Answer

Q37) 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 Show Answer

Q38) 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 Show Answer

Q39) 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 Show Answer

Q40) The point ( p+1, 1 ), (2p+1, 3 ) and ( 2p +2, 2p ) collinear, if Show Answer

Q41) 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 Show Answer

Q42) The sum of a + c is Show Answer

Q43) 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. Show Answer

Q44) 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 ). Show Answer

Q45) 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 Show Answer

Q46) 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 Show Answer

Q47) 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 Show Answer

Q48) 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 Show Answer