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If the point P(2, 2) is equidistant from the points A(–2, k) and B(–2k, –3), find k. Also, find the length of AP.
Concept: Distance Formula
In a classroom, 4 friends are seated at the points A, B, C and D as shown in the following figure. Champa and Chameli walk into the class and after observing for a few minutes, Champa asks Chameli, “Don’t you think ABCD is a square?” Chameli disagrees.
Using distance formula, find which of them is correct.
Concept: Distance Formula
For what values of k are the points (8, 1), (3, –2k) and (k, –5) collinear ?
Concept: Distance Formula
The long and short hands of a clock are 6 cm and 4 cm long respectively. Find the sum of the distances travelled by their tips in 24 hours. (Use π = 3.14) ?
Concept: Distance Formula
If A and B are the points (−6, 7) and (−1, −5) respectively, then the distance
2AB is equal to
Concept: Distance Formula
Find the value of y for which the distance between the points A (3, −1) and B (11, y) is 10 units.
Concept: Distance Formula
The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is ______.
Concept: Distance Formula
Find the distance between the points (a, b) and (−a, −b).
Concept: Distance Formula
The points (– 4, 0), (4, 0), (0, 3) are the vertices of a ______.
Concept: Distance Formula
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Case Study Trigonometry in the form of triangulation forms the basis of navigation, whether it is by land, sea or air. GPS a radio navigation system helps to locate our position on earth with the help of satellites. |
- Make a labelled figure on the basis of the given information and calculate the distance of the boat from the foot of the observation tower.
- After 10 minutes, the guard observed that the boat was approaching the tower and its distance from tower is reduced by 240(`sqrt(3)` - 1) m. He immediately raised the alarm. What was the new angle of depression of the boat from the top of the observation tower?
Concept: Distance Formula
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In a GPS, The lines that run east-west are known as lines of latitude, and the lines running north-south are known as lines of longitude. The latitude and the longitude of a place are its coordinates and the distance formula is used to find the distance between two places. The distance between two parallel lines is approximately 150 km. A family from Uttar Pradesh planned a round trip from Lucknow (L) to Puri (P) via Bhuj (B) and Nashik (N) as shown in the given figure below.
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Based on the above information answer the following questions using the coordinate geometry.
- Find the distance between Lucknow (L) to Bhuj (B).
- If Kota (K), internally divide the line segment joining Lucknow (L) to Bhuj (B) into 3 : 2 then find the coordinate of Kota (K).
- Name the type of triangle formed by the places Lucknow (L), Nashik (N) and Puri (P)
[OR]
Find a place (point) on the longitude (y-axis) which is equidistant from the points Lucknow (L) and Puri (P).
Concept: Distance Formula
The distance between the points (0, 5) and (–3, 1) is ______.
Concept: Distance Formula
Read the following passage:
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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 street on which there is a library. They both study in the same school and that is not far from Shagun's house. Suppose the school is situated at the point O, i.e., the origin, Alia's house is at A. Shagun's house is at B and library is at C. |
Based on the above information, answer the following questions.
- How far is Alia's house from Shagun's house?
- How far is the library from Shagun's house?
- Show that for Shagun, school is farther compared to Alia's house and library.
OR
Show that Alia’s house, shagun’s house and library for an isosceles right triangle.
Concept: Distance Formula
The distance of the point (5, 0) from the origin is ______.
Concept: Distance Formula
A point (x, y) is at a distance of 5 units from the origin. How many such points lie in the third quadrant?
Concept: Distance Formula
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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 is represented as points on a coordinate plane. |
- At an instance, the midfielders and forward formed a parallelogram. Find the position of the central midfielder (D) if the position of other players who formed the parallelogram are :- A(1, 2), B(4, 3) and C(6, 6)
- Check if the Goal keeper G(–3, 5), Sweeper H(3, 1) and Wing-back K(0, 3) fall on a same straight line.
[or]
Check if the Full-back J(5, –3) and centre-back I(–4, 6) are equidistant from forward C(0, 1) and if C is the mid-point of IJ. - If Defensive midfielder A(1, 4), Attacking midfielder B(2, –3) and Striker E(a, b) lie on the same straight line and B is equidistant from A and E, find the position of E.
Concept: Distance Formula
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(cosec θ – cot θ)^2 = (1-cos theta)/(1 + cos theta)`
Concept: Trigonometric Identities (Square Relations)
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(sin theta-2sin^3theta)/(2cos^3theta -costheta) = tan theta`
Concept: Trigonometric Identities (Square Relations)
If `tan theta = 24/7`, find that sin θ + cos θ.
Concept: Trigonometric Ratios
Prove the following trigonometric identities.
`(1 + sec theta)/sec theta = (sin^2 theta)/(1 - cos theta)`
Concept: Trigonometric Identities (Square Relations)
