Find the distance between the points C(2, 2) and D(5, 6).

1. Analyze the Question

We are asked to find the distance between two points on a Cartesian plane: $C(2, 2)$ and $D(5, 6)$.

2. Explain the Concept

To find the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$, we use the Distance Formula, which is derived from the Pythagorean theorem:

3. Show the Solution

• Step 1: Identify the coordinates. • Point $C(x_1, y_1) = (2, 2)$ • Point $D(x_2, y_2) = (5, 6)$

• Step 2: Substitute the values into the formula. $$d = \sqrt{(5 - 2)^2 + (6 - 2)^2}$$

• Step 3: Simplify the expressions inside the brackets. $$d = \sqrt{(3)^2 + (4)^2}$$

• Step 4: Calculate the squares. $$d = \sqrt{9 + 16}$$

• Step 5: Add and find the square root. $$d = \sqrt{25}$$ $$d = 5$$

4. Identify the Answer

The distance between the two points is 5 units. This corresponds to option D.

5. Exam Tip

Whenever you see coordinates involving small integers like 3 and 4, always look out for a 3-4-5 Pythagorean triple. Recognizing these common triangles can save you time during your JAMB exam, as you won't always need to write out the full calculation!