## Coordinate Geometry

### Important Questions

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 the diagram to…

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) 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) 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…