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Ahmad, a student of class IX, is residing in a village. One day, he

went to metro mall along with his brother. From there, he visited

three places library, temple and grocery shop. After returning to

his village, he plotted a graph by taking the metro mall as origin

and marked three places on the graph as per his direction of

movement and distance. The graph is given below.

(a) What are the coordinates of the temple?

(b) What is abscissa point of the library?

(c) What is the coordinates of grocery shop?

(d) What is the distance between temple and grocery shop?

Let's analyze the graph provided and answer each of the questions based on the locations marked.

1. **Coordinates of the temple:**
   - The temple is located at \((0, 3)\). The temple is directly above the origin (Metro Mall) on the \(y\)-axis.

2. **Abscissa (x-coordinate) of the library:**
   - The library is located at \((5, 2)\). The abscissa or \(x\)-coordinate of the library is \(5\).

3. **Coordinates of the grocery shop:**
   - The grocery shop is located at \((4, 0)\).

4. **Distance between the temple and grocery shop:**
   - To find the distance between the temple \((0, 3)\) and the grocery shop \((4, 0)\), we use the distance formula:
   \[
   \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
   \]
   Substituting the coordinates:
   \[
   \text{Distance} = \sqrt{(4 - 0)^2 + (0 - 3)^2} = \sqrt{4^2 + (-3)^2} = \sqrt{16 + 9} = \sqrt{25} = 5
   \]
   So, the distance between the temple and the grocery shop is \(5\) units.

Would you like further details or have any questions?

Here are five additional related questions for further exploration:

1. What is the ordinate (y-coordinate) of the library?
2. How would the coordinates change if the grocery shop moved 2 units to the left?
3. What would be the new coordinates of the temple if it were shifted 3 units down?
4. How can you find the midpoint between the grocery shop and the temple?
5. If Ahmad walked from the Metro Mall to the library and then directly to the temple, what is the total distance he walked?

**Tip:** The abscissa represents the x-coordinate, while the ordinate represents the y-coordinate in a coordinate plane.

Explore how to find coordinates and distances on a graph depicting locations like a temple, library, and grocery shop. Learn about coordinate geometry and apply the distance formula to calculate distances between points. Suitable for Grades 7-9 students.

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