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

Question 5

Step 1: We are given three vertices of the rectangle: \(A(0,3)\), \(O(0,0)\), and \(B(5,0)\).

Step 2: To find the diagonal, we need to connect vertex \(A\) to vertex \(B\). So, we will calculate the distance between points \(A(0,3)\) and \(B(5,0)\).

Step 3: 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 4: Substitute the coordinates of \(A(0,3)\) and \(B(5,0)\): \[ d = \sqrt{(5 - 0)^2 + (0 - 3)^2} \]

Step 5: Simplify each part: \((5 - 0)^2 = 5^2 = 25\) \((0 - 3)^2 = (-3)^2 = 9\)

Step 6: Add them together: \(25 + 9 = 34\)

Step 7: Take the square root: \[ d = \sqrt{34} \]

Final Answer: The length of the diagonal is \(\sqrt{34}\). So, the correct option is C.