Class 10 Case study of Chapter 7 coordinate geometry
Case study:1
To conduct Annual day activities, in a rectangular shaped school ground PQRS, lines have been drawn with chalk powder at a distance of 1 m each. 10 banners have been placed at a distance of 10 m from each other along PS. The first three banners have been shown in the graph along PS.
Three students Amit(A), Bhanu(B) and Chirag(C). Amit runs 1/5 th the distance PS on the first line and posts a blue flag. Bhanu runs 1/10 th the distance PS on the third line and posts a green flag. Chirag runs half the distance PS on the fifth line and posts a red flag.
(A) Find the coordinates of positions of blue, green and red flags.
(B) Find the distance between the blue and green flags.
Solution:
(A) Since, 10 banners have been placed at a distance of 10 m from each other along PS,
∴ Distance PS = 10×10 = 100 m
Now Amit runs distance along PS on first line and post a blue flag.
∴ Coordinates of position of blue flag = (1, )
= (1, 20)
Similarly, coordinates of green flag = (3, )
= (3, 10)
And coordinates of red flag = (5, )
= (5, 50)
(B) The coordinates of the blue and green flags are (1, 20) and (3, 10) respectively.
Applying the distance formula, the distance between the blue and green flags is:
m.
Case study:2
A farmer has plot of land in the shape of a quadrilateral as shown below:
(A) Find the image of the vertex A on the y-axis.
(B) Find the distances BC and CD.
Solution:
(A) The image of any point on the y-axis will have the same y-coordinate, but its x-coordinate will be negative of its earlier value. As coordinates of its image on y-axis wiill be (4, 5).
(B) From the graph,
B = (0, 7), C = (5, -5), D = (-4, -2)
∴ Using distance formula.
units
And
units.
Case study:3
Class X students of a secondary school in Krishnagar have been alloted a rectangular plot of a land for gardening activity. Saplings of Gulmohar are planted on the boundary at a distance of 1 m from each other. There is a triangular grassy lawn in the plot as shown in the figure. The students are to sow seeds of flowering plants on the remaining area of the plot.
(A) Considering A as the origin, what are the coordinates of A ?
(a) (0, 1) (b) (1, 0)
(c) (0, 0) (d) (-1, -1)
(B) What are the coordinates of P ?
(a) (4, 6) (b) (6, 4)
(c) (4, 5) (d) (5, 4)
(C) What are the coordinates of R ?
(a) (6, 5) (b) (5, 6)
(c) (6, 0) (d) (7, 4)
(D) What are the coordinates of D ?
(a) (16, 0) (b) (0, 0)
(c) (0, 16) (d) (16, 1)
(E) What are the coordinates of P, If D is taken as the origin ?
(a) (12, 2) (b) (-12, 6)
(c) (12, 3) (d) (6, 10)
Solution:
(A) Answer (c) (0, 0)
(B) Answer (a) (4, 6)
(C) Answer (a) (6, 5)
(D) Answer (a) (16, 0)
(E) Answer (b) (-12, 6)
Some other Case study question:
5: Arithmetic progression
Class 10 Case based problem of Chapter 5 A.P. 1
Class 10 Case based problem of Chapter 5 A.P. 2