Find the distance of the following points from origin :
(i) (3, -4)
(ii) (-8, -6)
(iii) (5, 12)
(iv) (7, 24)

Answer

To find the distance of the given points from the origin (0, 0), we will use the distance formula:

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

Where \((x_1, y_1)\) is the origin (0, 0) and \((x_2, y_2)\) is the point we are considering.

### Step-by-Step Solution:

**(i) For the point (3, -4):**

1. Identify the coordinates:
- \(x_1 = 0\), \(y_1 = 0\) (origin)
- \(x_2 = 3\), \(y_2 = -4\)

2. Apply the distance formula:
\[ d = \sqrt{(3 - 0)^2 + (-4 - 0)^2} \]

3. Calculate:
\[ d = \sqrt{3^2 + (-4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \]

**Distance from origin to (3, -4) is 5.**

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**(ii) For the point (-8, -6):**

1. Identify the coordinates:
- \(x_1 = 0\), \(y_1 = 0\) (origin)
- \(x_2 = -8\), \(y_2 = -6\)

2. Apply the distance formula:
\[ d = \sqrt{(-8 - 0)^2 + (-6 - 0)^2} \]

3. Calculate:
\[ d = \sqrt{(-8)^2 + (-6)^2} = \sqrt{64 + 36} = \sqrt{100} = 10 \]

**Distance from origin to (-8, -6) is 10.**

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**(iii) For the point (5, 12):**

1. Identify the coordinates:
- \(x_1 = 0\), \(y_1 = 0\) (origin)
- \(x_2 = 5\), \(y_2 = 12\)

2. Apply the distance formula:
\[ d = \sqrt{(5 - 0)^2 + (12 - 0)^2} \]

3. Calculate:
\[ d = \sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13 \]

**Distance from origin to (5, 12) is 13.**

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**(iv) For the point (7, 24):**

1. Identify the coordinates:
- \(x_1 = 0\), \(y_1 = 0\) (origin)
- \(x_2 = 7\), \(y_2 = 24\)

2. Apply the distance formula:
\[ d = \sqrt{(7 - 0)^2 + (24 - 0)^2} \]

3. Calculate:
\[ d = \sqrt{7^2 + 24^2} = \sqrt{49 + 576} = \sqrt{625} = 25 \]

**Distance from origin to (7, 24) is 25.**

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### Summary of Distances:
- Distance from (3, -4) to origin: **5**
- Distance from (-8, -6) to origin: **10**
- Distance from (5, 12) to origin: **13**
- Distance from (7, 24) to origin: **25**