NCERT Class X Chapter 7: Coordinate Geometry Exercise 7.1 Question 2

NCERT Class X Chapter 7: Coordinate Geometry

Question:

Find the distance between the points (0, 0) and (36, 15). Can you now find the distance between the two towns A and B, where town B is located 36 km east and 15 km north of the town A?

Given:

  • Point A: (0, 0)
  • Point B: (36, 15)
  • Town B is 36 km east and 15 km north of town A

To Find:

  • The distance between the points (0, 0) and (36, 15)
  • The distance between town A and town B

Formula:

Distance between two points \( (x_1, y_1) \) and \( (x_2, y_2) \):

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Solution:

Step 1: Let the points be \( A(0, 0) \) and \( B(36, 15) \).

Step 2: Apply the distance formula:

$$ AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Here, \( x_1 = 0,\, y_1 = 0,\, x_2 = 36,\, y_2 = 15 \).

Step 3: Substitute the values into the formula:

$$ AB = \sqrt{(36 - 0)^2 + (15 - 0)^2} $$

Step 4: Simplify the squares:

$$ AB = \sqrt{36^2 + 15^2} $$ $$ AB = \sqrt{1296 + 225} $$

Step 5: Add the values inside the square root:

$$ AB = \sqrt{1521} $$

Step 6: Find the square root:

$$ AB = 39 $$

Step 7: Therefore, the distance between the points \( (0, 0) \) and \( (36, 15) \) is 39 units. Since the towns are located with the same coordinates (in km), the distance between town A and town B is 39 km.

Result:

The distance between the points \( (0, 0) \) and \( (36, 15) \) is 39 units. The distance between town A and town B is 39 km.

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