Coordinate Geometry

CBSE Class 10 Mathematics · 107 board questions from this chapter; 105 listed below, 2022–2026

• The line segment joining the points P(-4,-2) and Q(10,4) is divided by y-axis in the ratio2026
• The mid-point of the line segment joining the points (5,-4) and (6,4) lies on:2026
• A circle centred at (-1, 2) passes through the point (0, 3). Radius of the circle is2026
• The distance of the point A(4 a, 3 a) from x -axis is:2026
• If the distance between the points (4, p) and (1,0) is 5, then p is equal to:2026
• If the distance between the points (4, p) and (1, 0) is 5, what is the value of p?2026
• Do the points P(1,0), Q(-5,0) and R(-2,5) form a triangle? If so, name the type of triangle formed.2026
• Diagonals AC and BD of square ABCD intersect at P. Coordinates of points B and D are (9, -2) and (1,6) respectively. (i) Find the…2026
• The coordinates of the centre of a circle are ( x-7,2 x ). Find the value(s) of ' x ', if the circle passes through the point (…2026
• If the points A(4, 5), B(m, 6), C(4, 3) and D(1, n) taken in this order are the vertices of a parallelogram ABCD, then find the…2026
• A point P divides the line segment joining the points A(-3,5) and B(7, -4) in a certain ratio. If the point P lies on the line…2026
• Find the ratio in which the x -axis divides the line segment joining the points (-6, 5) and (-4, -1). Also, find the point of…2026
• Find the coordinates of the points of trisection of the line segment joining the points A(-1, 4) and B(-3, -2).2026
• Determine the ratio in which the line 3 x+y-9=0 divides the line segment joining the points (1,3) and (2,5). Find the point of…2026
• A circle centered at (2,1) passes through the points A(5, 6) and B(-3, K). Find the value(s) of K. Hence find length of chord AB.…2026
• The three vertices of a rhombus PQRS are P(2,-3), Q(6,5) and R(-2,1). Find the coordinates of the fourth vertex S and coordinates…2026
• A point P(x, 7) divides a line segment joining the points A(-5,4) and B(7, 9) in a certain ratio. Find the ratio and hence find…2026
• Parthi and Alisha found a treasure that is exactly on the straight line joining their locations. Parthi's location is at point (-…2026
• Determine graphically, the coordinates of vertices of a triangle whose equations are 2 x-3 y+6=0; 2 x+3 y-18=0 and x=0. Also,…2026
• Observe the map of Jaipur city placed on a Cartesian plane. Taking Rambagh Palace as origin, the location of some places are…2026
• Observe the map of Jaipur city placed on a Cartesian plane. Taking Rambagh Palace as origin, the location of some places are…2026
• The distance of the point (4,0) from x -axis is:2025
• The mid-point of the line segment joining the points P(-4,5) and Q(4,6) lies on:2025
• The perimeter of the triangle formed by the vertices (0, 0), (2,0) and (0,2) is:2025
• The distance of a point A from x -axis is 3 units. Which of the following cannot be coordinates of the point A?2025
• The distance of the point A(-3, -4) from x -axis is2025
• The coordinates of the end points of a diameter of a circle are (5, -2) and (5, 2). The length of the radius of the circle is:2025
• The distance of which of the following points from origin is less than 5 units?2025
• The equation of a line parallel to y -axis and at a distance of 5 units to the right of y -axis is:2025
• The points (- 5, 0), (5, 0) and (0, 4) are the vertices of a triangle which is a/an:2025
• In the figure given below, points P, Q, R divides the line segment AB in four equal parts. The point Q divides PB in the ratio2025
• The point P divides the line segment AB in the ratio 3: 1 as shown below: The value of AB/PB is2025
• The line represented by x/4+y/6=1, intersects x -axis and y -axis respectively at P and Q. The coordinates of the mid-point of…2025
• Two of the vertices of Δ PQR are P(-1,5) and Q(5,2). The coordinates of a point which divides PQ in the ratio 2: 1 are:2025
• The distance of point (a, -b) from x -axis is2025
• The distance of point P(1,-1) from x -axis is:2025
• The distance of point P(3 a, 4 a) from y -axis is2025
• If the mid-point of the line segment joining the points (a, 4) and (2, 2b) is ( 2,6 ), then the value of ( a+b ) is given by:2025
• In the following figure, P and Q are points of trisection of line segment AB: the value of AB/PB=2025
• The end points of a diameter of circle are (2, 4) and (- 3, - 1). The length of its radius is:2025
• AOBC is a rectangle whose three vertices are A (0,2), O (0,0) and B (4,0). The square of the length of its diagonal is equal to:2025
• The equation of a line parallel to the x-axis and at a distance of 3 units below x-axis is:2025
• The coordinates of the end points of the line segment AB are A(-2, -2) and B(2,-4). P is the point on AB such that BP=4/7 AB.…2025
• Find the coordinates of the point C which lies on the line AB produced such that AC=2 BC, where coordinates of points A and B are…2025
• Prove that abscissa of a point P which is equidistant from points with coordinates A(7, 1) and B(3, 5) is 2 more than its…2025
• Find the length of the median through the vertex B of ABC with vertices A(9, -2), B(-3, 7) and C(-1, 10).2025
• If the mid-point of the line segment joining the points A(3, 4) and B(k, 6) is P(x, y) and x+y-10=0, find the value of k. OR Find…2025
• If (a, b) is the mid-point of the line segment joining the points A(10, - 6) and B(k, 4) and a-2 b=18, then find the value of k.2025
• Find the ratio in which the y-axis divides the line segment joining the points (5, -6) and (-1, -4). Also find the point of…2025
• P(x, y), Q(-2,-3) and R(2,3) are the vertices of a right triangle PQR right angled at P. Find the relationship between x and y.…2025
• If the mid-point of the line segment joining the points A(3,4) and B(k, 6) is P(x, y) and x+y-10=0, then find the value of k.2025
• Find a relation between x and y such that P(x, y) is equidistant from the points A(3, 5) and B(7, 1). Hence, write the…2025
• If the points A(6,1), B(p, 2), C(9,4) and D(7, q) are the vertices of a parallelogram ABCD, then find the values of p and q.…2025
• Point P divides the line segment joining the points A(4, -5) and B(1, 2) in the ratio 5:2. Co-ordinates of point P are2024
• AD is a median of ABC with vertices A(5, -6), B(6,4) and C(0, 0). Length AD is equal to:2024
• If the diagonals of a quadrilateral divide each other proportionally, then it is a:2024
• If the distance between the points (3, -5) and (x,-5) is 15 units, then the values of x are:2024
• XOYZ is a rectangle with vertices X(-3, 0), O(0, 0), Y(0, 4) and Z(x, y). The length of its each diagonal is2024
• The fourth vertex D of a parallelogram ABCD whose three vertices are A(-2,3), B(6,7) and C(8,3) is:2024
• The centre of a circle is at (2,0). If one end of a diameter is at (6,0), then the other end is at:2024
• Assertion (A): Mid-point of a line segment divides the line segment in the ratio 1: 1. Reason(R): The ratio in which the point (…2024
• Assertion: The point which divides the line segment joining the points A(1,2) and B(-1,1) internally in the ratio 1: 2 is (-1/3,…2024
• Find the type of triangle ABC formed whose vertices are A(1, 0), B(-5, 0) and C(-2, 5).2024
• Find a relation between x and y such that the point P(x, y) is equidistant from the points A(7, 1) and B(3, 5). OR Points A(-1,…2024
• Find the ratio in which the point P(-4,6) divides the line segment joining the points A(-6,10) and B(3, -8). OR Prove that the…2024
• The vertices of a ABC are A(-2,4), B(4,3) and C(1,-6). Find length of the median BD.2024
• In what ratio is the line segment joining the points (3, -5) and (-1, 6) divided by the line y=x? OR A(3,0), B(6,4) and C(-1,3)…2024
• Find the ratio in which the point (8/5, y) divides the line segment joining the points (1,2) and (2,3). Also, find the value of…2024
• In what ratio does the X-axis divides the line segment joining the points(2, -3) and (5,6)? Also, find the coordinates of the…2024
• Find the ratio in which the line segment joining the points (5,3) and (-1, 6) is divided by Y-axis. OR P(-2,5) and Q(3,2) are two…2024
• Through the mid-point M of the side CD of a parallelogram ABCD, the line BM is drawn intersecting AC in L and AD produced in E.…2024
• Ryan, from a very young age, was fascinated by the twinkling of stars and the vastness of space. He always dreamt of becoming an…2024
• A garden is in the shape of a square. The gardener grew saplings of Ashoka tree on the boundary of the garden at the distance of…2024
• The distance between the points (0,5) and (-3, 1) is:2023
• The distance of the point (- 6, 8) from x -axis is2023
• The ratio in which the x-axis divides the line segment joining the points (-2, 3) and (6, -7) is:2023
• The distance of the point (-1,7) from x -axis is:2023
• In what ratio, does x -axis divide the line segment joining the points A(3, 6) and B(-12, -3)?2023
• The point of intersection of the line represented by 3 x-y=3 and y-axis is given by2023
• The coordinates of the vertex A of a rectangle ABCD whose three vertices are given as B(0,0), C(3,0) and D(0,4) are:2023
• The end-points of a diameter of a circle are (2,4) and (-3, -1). The radius of the circle is2023
• The distance between the points P(-11/3, 5) and Q(-2/3, 5) is:2023
• The distance of the point (-4,3) from y -axis is2023
• The point of intersection of the line represented by 3 x-y=3 and the y-axis is given by2023
• The distance between the points (0,2 √5) and (-2 √5, 0) is2023
• The distance of the point (-6,8) from origin is:2023
• If end points of a diameter of a circle are (-5, 4) and (1, 0), then the radius of the circle is:2023
• The coordinates of the point where the line 2 y=4 x+5 crosses x -axis is2023
• The area of the triangle formed by the line x/a+y/b=1 with the coordinate axes is:2023
• The points (-4,0),(4,0) and (0,3) are the vertices of a:2023
• Find the ratio in which the y -axis divides the line segment joining the points (5, -6) and (-1, -4).2023
• The line segment joining the points A(4,-5) and B(4,5) is divided by the point P such that AP: AB=2: 5. Find the coordinates of…2023
• Find the ratio in which line y=x divides the line segment joining the points (6, -3) and (1, 6).2023
• A line intersects y -axis and x -axis at point P and Q, respectively. If R(2,5) is the mid-point of line segment PQ, then find…2023
• Show that the points (-2, 3), (8,3) and (6,7) are the vertices of a right-angled triangle.2023
• Find the ratio in which y-axis divides the line segment joining the points (5,-6) and (-1, -4).2023
• Find the points on the x -axis, each of which is at a distance of 10 units from the point A(11, - 8).2023
• In the given figure, ABCD is a parallelogram. AE divides the line segment BD in the ratio 1: 2. If BE=1.5 cm, then find the…2023
• Find the ratio in which the line segment joining the points A(6,3) and B(-2, -5) is divided by x -axis.2023
• In the given figure, CD is the perpendicular bisector of AB. EF is perpendicular to CD. AE intersects CD at G. Prove that (C…2023
• If Q(0,1) is equidistant from P(5,-3) and R(x, 6), find the values of x.2023
• In the given figure, CD is the perpendicular bisector of AB. EF is perpendicular to CD. AE intersects CD at G. Prove that (C…2023
• If (-5,3) and (5,3) are two vertices of an equilateral triangle, then find co- ordinates of the third vertex, given that origin…2023
• Jagdish has a field which is in the shape of a right angled triangle AQC. He wants to leave a space in the form of a square PQRS…2023
• The tops of two poles of heights 20 m and 28 m are connected with a wire. The wire is inclined to the horizontal at an angle of…2022

Answers come from CBSE’s own marking schemes. How we source them.