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Q)Â 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 first time in the FIFA Women’s World Cup’s history, two nations host in 10 venues. Her father felt that the game can be better understood if the position of players […]
coordinate geometry
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 solve: Let’s consider the coordinates of point P is (0,y) Also consider that the line AB is divided in ratio of m : n. By section formula,
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 that PAÂ = PB Hence, PA2Â = PB2 Â Â (x – 5)2Â + (y – 1)2 = (x – 1)2 + (y – 5)2 – 10 x – 2y = –
Point P(x, y) is equidistant from points A(5, 1) and B(1, 5). Prove that x = y. Read More »
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. Find the coordinates of P. Ans: Let’s draw the diagram to solve: Given that  (AB = AP + PB) by cross multiplication, we get: 5 AP = 2 (AP
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 of a square PQRS inside the field for growing wheat and the remaining for growing vegetables (as shown in the figure). In the field, there is a pole marked as
Jagdish has a field which is in the shape of a right angled triangle AQC. Read More »
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 P & Q = Distance between R & Q Â (5-0) 2 + (-3-1) 2 = (x-0)2 + (6-1)2 or 25 +16 = x2 + 25 or x2 = 16
If Q(0,1) is equidistant from P(5,-3) and R (x,6), find the values of x. Read More »
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 on graph, we get: Step 1: Now for a Δ ABC to be an right angled triangle, required condition is: AB2 = AC2 + BC2 Step 2: Let’s calculate the
Q) Solve the pair of equations x = 5 and y = 7 graphically. Ans:Â Â Here is the answer to this question: For a detailed answer to this question, please refer to the similar question and its solution (click on the link below) Solve the pair of equations x = 3 and y =- 4
Solve the pair of equations x = 5 and y = 7 graphically. Read More »
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 circle is 5√2cm. Ans: Let’s find out radius of the circle by co-ordinate method. Therefore, (2a – 11)2 + (a -7 + 9)2 = (5√2 )2 or (4a2 + 121
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 triangle. (Take √3 = 1.7) Ans:  VIDEO SOLUTION STEP BY STEP SOLUTION Let the third vertex be (x, y)Hence, 3 vertex of the triangle will be A (-5,3)         B (5,3)         C