NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 7: Coordinate Geometry - Exercise 7.1

Question 4

We need to find the distance between the two points \((x_1, y_1) = (0,5)\) and \((x_2, y_2) = (-5,0)\).

Step 1: Recall the distance formula in a 2-D plane:

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

Step 2: Substitute the values:

\[ d = \sqrt{((-5) - 0)^2 + (0 - 5)^2} \]

Step 3: Simplify each term:

\[ d = \sqrt{(-5)^2 + (-5)^2} \]

\[ d = \sqrt{25 + 25} \]

Step 4: Add the terms inside the square root:

\[ d = \sqrt{50} \]

Step 5: Simplify the square root:

\[ d = \sqrt{25 \times 2} = 5\sqrt{2} \]

Final Answer: The distance between the two points is \(5\sqrt{2}\) units.

If we take 1 unit as 1 metre (SI unit of distance), the distance is \(5\sqrt{2}\, \text{m}\).