Let p, q, r, s be the distances from origin of the points (2, 6), (3, 4), (4, 5) and (-2, 5) respectively. Which one of the following is a whole number?

Options

A. p
B. q
C. r
D. s

Answer

To find the distances from the origin for the points (2, 6), (3, 4), (4, 5), and (-2, 5), we will use the distance formula. The distance from a point (x, y) to the origin (0, 0) is given by the formula:

\[ \text{Distance} = \sqrt{(x - 0)^2 + (y - 0)^2} = \sqrt{x^2 + y^2} \]

Let's calculate the distances step by step:

### Step 1: Calculate the distance for point A (2, 6)
Using the formula:
\[ OA = \sqrt{(2)^2 + (6)^2} \]
\[ OA = \sqrt{4 + 36} \]
\[ OA = \sqrt{40} \]

### Step 2: Calculate the distance for point B (3, 4)
Using the formula:
\[ OB = \sqrt{(3)^2 + (4)^2} \]
\[ OB = \sqrt{9 + 16} \]
\[ OB = \sqrt{25} \]
\[ OB = 5 \]

### Step 3: Calculate the distance for point C (4, 5)
Using the formula:
\[ OC = \sqrt{(4)^2 + (5)^2} \]
\[ OC = \sqrt{16 + 25} \]
\[ OC = \sqrt{41} \]

### Step 4: Calculate the distance for point D (-2, 5)
Using the formula:
\[ OD = \sqrt{(-2)^2 + (5)^2} \]
\[ OD = \sqrt{4 + 25} \]
\[ OD = \sqrt{29} \]

### Summary of Distances
- Distance OA = \( \sqrt{40} \)
- Distance OB = \( 5 \)
- Distance OC = \( \sqrt{41} \)
- Distance OD = \( \sqrt{29} \)

### Conclusion
Among the calculated distances, the only whole number is \( OB = 5 \).

### Final Answer
The whole number among the distances is \( Q = 5 \).

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