CBSE Class 10 Maths (Basic) 2024 · Paper 430/S/1 · Question 37

Coordinate Geometry 4 marks Very hard

Drones are used by military for surveillance purposes. These days, drones are also used by individual entrepreneurs, SMEs and large companies to accomplish various other tasks (disaster management, entertainment, law enforcement, wildlife monitoring, weather forecast, aerial photograph, shipping and delivery, geographical mapping, precision agriculture, search and rescue, etc.). A drone is flying over a rectangular field with vertices at A(-100, 0), B(100, 0), C(100, 150) and D(-100, 150). The drone captures an image at a location (x, y).

Applications of drones (block diagram)

Rectangular field on coordinate axes with vertices A, B, C, D

(i)Find the dimensions of the rectangular field.[1]
(ii)Find the distance between points A and C.[1]
(iii)(a)If a drone captures the image of an object $P (x, y)$ on the rectangular field, find the relation between $x$ and $y$ such that $P A = P C$ .[2]
(iii)(b)If a drone captures the image of an object at a point Q whose x-coordinate is 0 and it is equidistant from points A and D, find the coordinates of Q.[2]

Answer

(i) Length

A B = 200

units and breadth

B C = 150

units, so the field is

200 \times 150

units; (ii)

A C = 250

units; (iii)(a)

4 x + 3 y = 225

; (iii)(b)

Q (0, 75)

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From the board paper

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CBSE Class 10 Maths (Basic) 2024 · Paper 430/S/1 · Question 37

Answer

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