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

#### 6: Triangle

Class 10 Case based problem of Chapter 6 Triangles 1

Class 10 Case based problem of Chapter 6 Triangles 2