Practice Test

Q1) Find the distance between the points (3, 4) and (8, -6). Show Answer

Q2) Find the distance between the points (5, 2) and (0, 0). Show Answer

Q3) Find the value of p if the distnace between the points (8, p) and (4, 3) is 5. Show Answer

Q4) Find the value of c if the distance between the point (c, 4) and the origin is 5 units. Show Answer

Q5) Find the mid-point of the line segment made by joining the points (3, 2) and (6, 4). Show Answer

Q6) If the origin is the mid-point of the line segment joined by the points (2, 3) and (x, y) find the value of (x, y). Show Answer

Q7) Find the points that divide the line segment joining (2, 5) and (-1, 2) in the ratio 2 : 1 internally. Show Answer

Q8) In what ratio does the x-axis divide the line segment joining the points (2, -3) and (5, 6)? Show Answer

Q9) How many squares are possible if two of the vertices of a quadrilateral are (1, 0) and (2, 0)? Show Answer

Q10) If the point R (1, -2) divides externally the line segment joining P (2, 5) and Q in the ratio 3 : 4, what will be the coordinates of Q? Show Answer

Q11) Find the coordinates of the points that trisect the line segment joining (1, -2) and (-3, 4) Show Answer

Q12) Find the coordinates of the point that divides the line segment internally. Show Answer

Q13) Find the coordinates of the point if it divides the points externally. Show Answer

Q14) What ratio is the line segment joining? Show Answer

Q15) Find the nature of division? Show Answer

Q16) What ratio is the line segment divided by the y-axis? Show Answer

Q17) What is the nature of the division? Show Answer

Q18) If the coordinates of the mid-point of the line segment joining the points (2, 1) and (1, -3) is (x, y) then the relation between x and y can be best described by Show Answer

Q19) Points (6, 8), (3, 7), (-2, -2) and (1, -1) are joined to form a quadrilateral. What will be this structure? Show Answer

Q20) Points (4, -1), (6, 0), (7, 2) and (5, 1) are joined to be a vertex of a quadrilateral. What will be the structure? Show Answer

Q21) What will be the centroid of a triangle whose vertices are (2, 4), (6, 4) and (2, 0)? Show Answer

Q22) The distance between the lines 4 x + 3 y = 11 and 8 x + 6 y = 15 is Show Answer

Q23) If the mid-point of the line joining (3, 4) and (p, 7) is (x, y) and 2 x + 2 y + 1 = 0, then what will be the value of p? Show Answer

Q24) Find the third vertex of the triangle whose two vertices are (-3, 1) and (0, -2) and the centroid is the origin. Show Answer

Q25) Find the area of the triangle whose vertices are (1, 3), (-7, 6) and (5, -1). Show Answer

Q26) Find the area of the triangle whose vertices are (a, b + c), (a, b - c) and (-a, c). Show Answer

Q27) The number of lines that are parallel to 2 x + 6 y + 7 = 0 and have an intercept of length 10 between the coordinate axes is Show Answer

Q28) Which of the following three points represent a straight line? Show Answer

Q29) Which of the following will be the equation of a straight line that is parallel to the y-axis at a distance 11 units from it? Show Answer

Q30) Which of the following will be the equation of a straight line parallel to the y-axis at a distance of 9 units to the left? Show Answer

Q31) What can be said about the equation of the straight line x = 7? Show Answer

Q32) What can be said about the equation of the straight line y = -8? Show Answer

Q33) Which of the following straight lines passes through the origin? Show Answer

Q34) What will be the point of intersection of the equation of lines 2 x + 5 y = 6 and 3 x + 4 y = 7? Show Answer

Q35) If P (6, 7), Q (2, 3) and R (4, -2) be the vertices of a triangle, then which of the following is not a point contained in this triangle? Show Answer

Q36) What will be the reflection of the point (4, 5) in the second quadrant? Show Answer

Q37) What will be the reflection of the point (4, 5) in the third quadrant? Show Answer

Q38) If the origin gets shifted to (2, 2), then what will be the new coordinates of the point (4, -2)? Show Answer

Q39) What will be the length of the perpendicular drawn from the point (4, 5) upon the straight line 3 x + 4 y = 10? Show Answer

Q40) Find the area of the quadrilateral the coordinates of whose angular points taken in order are (1, 1), (3, 4), (5, -2) and (4, -7). Show Answer

Q41) Find the area of the quadrilateral the coordinates of whose angular points taken in order are (-1, 6), (-3, -9), (5, -8) and (3, 9). Show Answer

Q42) Two vertices of a triangle are (5, -1) and (-2, 3). If the orthocenter of the triangle is the origin, what will be the coordinates of the third point? Show Answer

Q43) Find the equation of the straight line passing through the origin and the point of intersection of the lines x/a + y/b = 1 and x/b + y/a = 1. Show Answer

Q44) One side of a rectangle lies along the line 4 x + 7 y + 5 = 0. Two of its vertices are (-3, 1) and (1, 1). Which of the following may be an equation which represents any of the other three straight lines? Show Answer

Q45) The points (p - 1, p + 2), (p, p + 1), (p + 1, p) are collinear for Show Answer

Q46) The straight line joining (1, 2) and (2, -2) is perpendicular to the line joining (8, 2) and (4, p). What will be the value of p? Show Answer

Q47) What will be the length of the perpendicular drawn from the point (-3, -4) to the straight line 12 (x + 6) = 5 (y - 2)? Show Answer

Q48) The area of the triangle with vertices at (a, b + c), (b, c + a) and (c, a + b) is Show Answer

Q49) Find the distance between the two parallel straight lines y = m x + c and y = m x + d? [Assume c > d] Show Answer

Q50) Find the equation of the straight line if it is perpendicular to the straight line 3 x - 4 y = 5? Show Answer

Q51) Find the equation of the straight line if it is parallel to the straight line 3 x + 4 y = 5? Show Answer

Q52) The orthocenter of the triangle formed by the points (0, 0), (8, 0) and (4, 6) is Show Answer

Q53) The area of a triangle is 5 square units, two of its vertices are (2, 1) and (3, -2). The third vertex lies on y = x + 3. What will be the third vertex? Show Answer

Q54) The equations of two equal sides AB and AC of an isosceles triangle ABC are x + y = 5 and 7 x - y = 3 respectively. What will be the equation of the side BC if area of triangle ABC is 5 square units. Show Answer

Q55) Three vertices of a rhombus, taken in order are (2, -1), (3, 4) and (-2, 3). Find the fourth vertex. Show Answer

Q56) Four vertices of a parallelogram taken in order are (-3, -1), (a, b), (3, 3) and (4, 3). What will be the ratio of a to b? Show Answer

Q57) What will be the new equation of straight line 3 x + 4 y = 6 if the origin gets shifted to (3, -4)? Show Answer

Q58) What will be the value of p if the equation of straight line 2 x + 5 y = 4 gets changed to 2 x + 5 y = p after shifting the origin at (3, 3)? Show Answer

Q59) A line passing through the points (a, 2a) and (-2, 3) is perpendicular to the line 4 x + 3 y + 5 = 0. Find the value of a? Show Answer

Q60) The area of a triangle is 5 square units. Two of its vertices are (2, 1) and (3, -2). The third vertex lies on y = x + 3. What will be the third vertex? Show Answer

Q61) One side of a rectangle lies along the line 4 x + 7 y + 5 = 0. Two of its vertices are (-3, 1) and (1, 1). Which of the following is not an equation of the other three straight lines? Show Answer

Q62) The area of triangle formed by the points (p, 2-2p), (1-p, 2p) and (-4-p, 6-2p) is 70 units. How many integral values of p are possible? Show Answer

Q63) What are the points on the axis of x whose perpendicular distance from the straight line x/p + y/q = 1 is p? Show Answer

Q64) If the medians PT and RS of a triangle with vertices P (0, b), Q (0, 0) and R (a, 0) are perpendicular to each other, which of the following satisfies the relationship between a and b? Show Answer

Q65) The point of intersection of the lines x/a + y/b = 1 and x/b + y/b = 1 lies on the line Show Answer

Q66) PQR is an isosceles triangle. If the coordinates of the base are Q (1, 3) and R (-2, 7), then the coordinates of the vertex P can be Show Answer

Q67) The extremities of a diagonal of a parallelogram are the points (3, -4) and (-6, 5). If the third vertex is the point (-2, 1), the coordinate of the fourth vertex is Show Answer

Q68) If the points (a, 0), (0, b) and (1, 1) are collinear then which of the following is true? Show Answer

Q69) If P and Q are two points on the line 3 x + 4 y = -15, such that OP = OQ = 9 units, the area of the triangle POQ will be Show Answer

Q70) If the coordinates of the points A, B, C and D are (6, 3), (-3, -5), (4, -2) and (a, 3a) respectively and if the ratio of the area of triangles ABC and DBC is 2 : 1, then the value of a is Show Answer

Q71) The equations of two equal sides AB and AC of an isosceles triangle ABC are x + y = 5 and 7 x - y = 3 respectively. What will be the length of the intercept cut the side BC on the y-axis? Show Answer

Q72) A line is represented by the equation 4 x + 5 y = 6 in the coordinate system with the origin (0, 0). You are required to find the equation of the straight line perpendicular to this line that passes through the point (1, -2) [which is in the coordinate system where origin is at (-2, -2)]. Show Answer

Q73) Two sides of a square lie on the lines x + y = 1 and x + y + 2 = 0. What is its area? Show Answer

Q74) Find the value of k if the straight line 2x + 3 y + 4 + k (6x - y + 12) = 0 is perpendicular to the line 7x + 5y = 4. Show Answer

Q75) How many points on x + y = 4 are there that lie at a unit distance from the line 4x + 3y = 10? Show Answer

Q76) The coordinates of the mid-points of the sides of a triangle are (4, 2), (3, 3) and (2, 2). What will be the coordinates of the centroid of the triangle? Show Answer

Q77) A wooden box (open at the top) of thickness 0.5 cm, length 21 cm, width 11 cm and height 6 cm is painted on the inside. The expenses of painting are Rs. 140. What is the rate of painting per square centimeter? Show Answer

Q78) Which one of the following cannot be the ratio of angles in a right-angled triangle? Show Answer

Q79) A slab of ice 10 inches in length, 15 inches in breadth, and 3 inches thick was melted and re-solidified in the form of a rod of 10 inches diameter. The length of such a rod, in inches, is nearest to: Show Answer

Q80) The area of the triangle whose vertices are (a, a), (a + 1, a + 1), (a + 2, a) is : Show Answer

Q81) In a rectangle, the difference between the sum of the adjacent sides and the diagonal is two-thirds the length of the shorter side. What is the ratio of the shorter to the longer side? Show Answer