## Coordinate Geometry

### Important Questions

Q) Find the length of the median AD of Δ ABC having vertices A(0, –1), B(2, 1) and C(0, 3). Ans: Let’s plot the points on…

Q) In what ratio does the X-axis divide the line segment joining the points(2, – 3) and (5, 6)? Also, find the coordinates of the…

Q) A garden is in the shape of a square. The gardener grew saplings of Ashoka tree on the boundary of the garden at the…

Q) Ryan, from a very young age, was fascinated by the twinkling of stars and the vastness of space. He always dreamt of becoming an astronaut…

Q) Find the point(s) on the x-axis which is at a distance of √41 units from the point (8, -5). Ans: Let the point be…

Q) Show that the points A(-5,6), B(3, 0) and C( 9, 8) are the vertices of an isosceles triangle. Ans: For a triangle to be…

Q) Solve the following system of linear equations graphically: x + 2 y = 3, 2 x – 3 y + 8 = 0 Ans:…

Q) Points A(–1, y) and B(5, 7) lie on a circle with centre O(2, –3y) such that AB is a diameter of the circle. Find…

Q) 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). Ans:…

Q) Solve the following system of linear equations graphically: 3 x – y + 1 = 0 x + y = 5 Ans: Step 1:…

Q) Find the ratio in which the line segment joining the points (5, 3) and (–1, 6) is divided by Y-axis. Ans: Step 1: By…

Q) P(–2, 5) and Q(3, 2) are two points. Find the coordinates of the point R on line segment PQ such that PR = 2QR.…

Q) Using graphical method, solve the following system of equations : 3 x – 2 y = 10 and 5 x + 3 y =…

Q) The vertices of Δ ABC are A (- 2, 4), B(4, 3) and C(1, – 6). Find length of the median BD. Ans: Let’s plot…

Q) 22. Find the type of triangle ABC formed whose vertices are A(1, 0), B(-5, 0) and C(-2, 5). Ans: Step 1: Let’s plot the…

Q) In what ratio is the line segment joining the points (3, – 5) and (- 1, 6) divided by the line y = x…

Q) A(3, 0), B(6, 4) and C(-1, 3) are vertices of a triangle ABC. Find length of its median BE. Ans: Let’s plot the points on…

Q) Prove that A(4, 3), B(6, 4), C(5, 6), D(3, 5) are the vertices of a square ABCD. Ans: Let’s plot the points on the graph:…

Q) Show that the points (-3, – 3), (3, 3) and (-3√3, 3√3) are the vertices of an equilateral triangle. Ans: Let’s consider the points…

Q) Find the ratio in which the point (- 1, k) divides the line segment joining the points (- 3, 10) and (6, – 8).…

Q) Draw the graph of the following equations: x + y = 5, x – y = 5, and (i) find the solution of the…

Q) Using graphical method, solve the following system of equations : 3x + y + 4 = 0 and 3 x – y + 2…

Q) ABCD is a rectangle formed by the points A (−1, −1), B (−1, 6), C (3, 6) and D (3, −1). P, Q, R…

Q) 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…

Q) The vertices of a quadrilateral ABCD are A(6, – 2), B(9, 2), C(5, – 1) and D(2, – 5). Prove that ABCD is a…

Q) In order to conduct Sports Day activities in your School, lines have been drawn with chalk powder at a distance of 1 m each,…

Q) Two rails are represented by the linear equations x + 2y – 4 = 0 and 2x + 4y – 12 = 0. Represent…

Q) If A and B are (-2, -2) and (2, -4) respectively, find the coordinates of P such that AP = AB and P lies…

Q) Two vertices of a triangle have coordinates (-8,7) and (9,4). If the centroid of the triangle is at the origin, what are the coordinates…

Q) Find the ratio in which line y = x divides the line segment joining the points (6, -3) and (1, 6). Ans: Let’s draw…

Q) Using Cartesian Coordinates we mark a point on a graph by how far along and how far up it is.The left-right (horizontal) direction is…

Q) Alia and Shagun are friends living on the same street in Patel Nagar. Shagun’s house is at the intersection of one street with another…

Q) Tharunya was thrilled to know that the football tournament is fixed with a monthly timeframe from 20th July to 20th August 2023 and for the…

Q) Find the ratio in which y-axis divides the line segment joining the points (5, – 6) and (- 1, – 4). Ans: Let’s draw…

Q) Point P(x, y) is equidistant from points A(5, 1) and B(1,5). Prove that x = y. Ans: Let’s draw the diagram to solve: Given…

Q) 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.…

Q) Jagdish has a field which is in the shape of a right angled triangle AQC. He wants to leave a space in the form…

Q) If Q(0,1) is equidistant from P(5,-3) and R (x,6), find the values of x. Ans: since the Point Q is equidistant, then Distance between…

Q) Show that the points (- 2, 3), (8, 3) and (6, 7) are the vertices of a right-angled triangle. Ans: Let’s plot these points…

Q)Solve the pair of equations x = 5 and y = 7 graphically. Ans: Plot both the equations on the graph. Increase till intersection point…

Q) The centre of a circle is (2a, a-7). Find the values of ‘a’ if the circle passes through the point (11,-9). Radius of the…

Q) Using graphical method, find whether following system of linear equations x = 0 and y = – 3 is consistent or not. Ans: Draw…

Q) If (-5,3) coordinates and (5,3) are two vertices of an equilateral triangle, then find of the third vertex, given that origin lies inside the…

Q) Solve the pair of equations x = 3 and y = – 4 graphically. Ans: Lets plot both the equations on the graph. Increase…