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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: undefined >> undefined
Find a and b so that the numbers a, 7, b, 23 are in A.P.
Concept: undefined >> undefined
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In an A.P. if the sum of third and seventh term is zero. Find its 5th term.
Concept: undefined >> undefined
Write the next two terms of the A.P.: `sqrt(27), sqrt(48), sqrt(75)`......
Concept: undefined >> undefined
The number of quadratic polynomials having zeroes –5 and –3 is ______.
Concept: undefined >> undefined
If α and β are the zeroes of the polynomial x2 – 1, then the value of (α + β) is ______.
Concept: undefined >> undefined
The distance between the points (0, 5) and (–3, 1) is ______.
Concept: undefined >> undefined
The zeroes of the polynomial 3x2 + 11x – 4 are ______.
Concept: undefined >> undefined
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: undefined >> undefined
Show that Alia's house, Shagun's house and library for an isosceles right triangle.
Concept: undefined >> undefined
Read the following passage:
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Use of mobile screen for long hours makes your eye sight weak and give you headaches. Children who are addicted to play "PUBG" can get easily stressed out. To raise social awareness about ill effects of playing PUBG, a school decided to start 'BAN PUBG' campaign, in which students are asked to prepare campaign board in the shape of a rectangle: One such campaign board made by class X student of the school is shown in the figure.
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Based on the above information, answer the following questions:
- Find the coordinates of the point of intersection of diagonals AC and BD.
- Find the length of the diagonal AC.
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- Find the area of the campaign Board ABCD.
OR - Find the ratio of the length of side AB to the length of the diagonal AC.
- Find the area of the campaign Board ABCD.
Concept: undefined >> undefined
The number of polynomials having zeroes – 3 and 4 is ______.
Concept: undefined >> undefined
The distance of the point (5, 0) from the origin is ______.
Concept: undefined >> undefined
The graph of y = f(x) is shown in the figure for some polynomial f(x).
The number of zeroes of f(x) is ______.
Concept: undefined >> undefined
The zeroes of the quadratic polynomial 16x2 – 9 are ______.
Concept: undefined >> undefined
The graph of y = f(x) is shown in the figure for some polynomial f(x). The number of zeroes of f(x) are ______.
Concept: undefined >> undefined
The given linear polynomial y = f(x) has
Concept: undefined >> undefined
A point (x, y) is at a distance of 5 units from the origin. How many such points lie in the third quadrant?
Concept: undefined >> undefined
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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: undefined >> undefined
If α and β are the zeroes of the polynomial x2 + x − 2, then find the value of `alpha/beta+beta/alpha`
Concept: undefined >> undefined
