NCERT Class X Chapter 7: Coordinate Geometry Exercise 7.1 Question 1(i)

NCERT Class X Chapter 7: Coordinate Geometry

Question:

Find the distance between the points (2, 3) and (4, 1).

Given:

Points: \((x_1, y_1) = (2, 3)\), \((x_2, y_2) = (4, 1)\)

To Find:

The distance between the two given points.

Formula:

The distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

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

Solution:

Step 1: Substitute the given values into the distance formula.

$$ d = \sqrt{(4 - 2)^2 + (1 - 3)^2} $$

Step 2: Calculate the differences.

$$ d = \sqrt{(2)^2 + (-2)^2} $$

Step 3: Square the differences.

$$ d = \sqrt{4 + 4} $$

Step 4: Add the results inside the square root.

$$ d = \sqrt{8} $$

Step 5: Simplify the square root.

$$ d = \sqrt{4 \times 2} = 2\sqrt{2} $$

Result:

The distance between the points (2, 3) and (4, 1) is \(2\sqrt{2}\).

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