Class 10 Case study of Chapter 7 coordinate geometry
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.
(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:
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.
(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.
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)
(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)