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

NCERT Class X Chapter 7: Coordinate Geometry

Question:

Find the distance between the points \((a, b)\) and \((-a, -b)\).

Given:

Two points: \((a, b)\) and \((-a, -b)\)

To Find:

The distance between the points \((a, b)\) and \((-a, -b)\).

Formula:

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

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

Solution:

Step 1: Let \((x_1, y_1) = (a, b)\) and \((x_2, y_2) = (-a, -b)\).

Step 2: Substitute the values into the distance formula:

$$ \sqrt{((-a) - a)^2 + ((-b) - b)^2} $$

Step 3: Simplify the expressions inside the square root:

$$ \sqrt{(-2a)^2 + (-2b)^2} $$

Step 4: Calculate the squares:

$$ \sqrt{4a^2 + 4b^2} $$

Step 5: Factor out 4 from the square root:

$$ \sqrt{4(a^2 + b^2)} $$

Step 6: Take the square root of 4:

$$ 2\sqrt{a^2 + b^2} $$

Result:

The distance between the points \((a, b)\) and \((-a, -b)\) is:

$$ 2\sqrt{a^2 + b^2} $$
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