coordinate geometry

Q) Vertices of a right triangle ABC with ∠ B = 90 are A (3, 4), B (1, 1) and C (- 8,7) Find the value of tan A. (Q 25 A – 30/5/2 – CBSE 2026 Question Paper) Ans: [Approach: to find value of tan A, we need to find length of CB and […]

Q) Using distance formula, prove that the points A (2, 3), B (- 7, 0) and C (- 1,2) are collinear. (Q 25 B – 30/5/2 – CBSE 2026 Question Paper) Ans: [Approach: To prove that three points are collinear using the distance formula, we must show that the distance between first two points plus

Q) A circle centered at (2, 1) passes through the points A (5, 6) and B (- 3, k) Find the value of k. Hence find length of chord. (Q 26 A – 30/5/2 – CBSE 2026 Question Paper) Ans: (i) Value of k: Let (2, 1) be the center O. If points A and

Q) Prove that the point P dividing the line segment joining the points A (- 1, 7) and B (4, – 3) in the ratio 3: 2, lies on the line x – 3y = – 1. (Q 26 B – 30/5/2 – CBSE 2026 Question Paper) Ans: (i) Verifying if P lies on line

Q) Observe the map of Jaipur city placed on a Cartesian plane. Taking Rambagh Palace as origin, the location of some places are given below: Point A: (−4, 2) Rajasthan High CourtPoint B: (4, −4) Birla MandirPoint C: (4, 3) Heera BaghPoint D: (−5, −2) Amar Jawan JyotiBased on the above, answer the following questions:(i).

Q) 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 co-ordinates of point P. (ii) Find the length of the side of the square. (Q 25A – 30/3/3 – CBSE 2026 Question Paper) Ans: (i) Co-ordinates of

Q) Find the coordinates of a point on the line x + y = 5 which is equidistant from (6, 4) and (5, 2). (Q 25B – 30/3/3 – CBSE 2026 Question Paper) Ans: Let the coordinates of the this point be (x, y) Step 1: Since this point lies on equation, it will satisfy

Q) Determine the ratio in which the line 3x + y – 9 = 0 divides the line segment joining the points (1, 3) and (2, 5). Find the point of intersection. (Q 28 – 30/3/3 – CBSE 2026 Question Paper) Ans: (i) calculating for division ratio Step 1: Let’s consider the given points are

Q) Determine graphically, the coordinates of vertices of a triangle whose equations are 2x − 3y + 6 = 0; 2x + 3y − 18 = 0 and x = 0. Also, find the area of this triangle (Q32 – 30/1/1 – CBSE 2026 Question Paper) Ans:  Step 1: We have following equations of the

Q) Do the points P (1, 0), Q (-5, 0) and R (-2, 5) form a triangle ? If so, name the type of triangle formed. (Q21 – 30/1/3 – CBSE 2026 Question Paper) Ans:  Step 1: Let’s first understand the question: By Triangle Inequality Property, We know that to form a triangle, the sum