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

Question 3

We want to find the distance of the point \(P(-6,8)\) from the origin \((0,0)\).

Step 1: Recall the distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\):

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

Step 2: Here the origin is \((0,0)\) and the point is \((-6,8)\).

So, \(x_1 = 0,\; y_1 = 0,\; x_2 = -6,\; y_2 = 8\).

Step 3: Substitute these values into the formula:

\[ d = \sqrt{(-6 - 0)^2 + (8 - 0)^2} \]

Step 4: Simplify each term:

\((-6 - 0)^2 = (-6)^2 = 36\)

\((8 - 0)^2 = (8)^2 = 64\)

Step 5: Add the results:

\[ d = \sqrt{36 + 64} = \sqrt{100} \]

Step 6: Find the square root:

\[ d = 10 \]

Final Answer: The distance is 10 units. So the correct option is C.