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:

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

In this case, since we are measuring the distance from the origin, we can take \( (x_1, y_1) \) as \( (0, 0) \) and \( (x_2, y_2) \) as the coordinates of the point.

### Step-by-Step Solution:

1. **Distance from (3, -4)**:
- Using the distance formula:
\[ d_1 = \sqrt{(3 - 0)^2 + (-4 - 0)^2} \]
- Calculate:
\[ d_1 = \sqrt{3^2 + (-4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \]

2. **Distance from (-8, -6)**:
- Using the distance formula:
\[ d_2 = \sqrt{(-8 - 0)^2 + (-6 - 0)^2} \]
- Calculate:
\[ d_2 = \sqrt{(-8)^2 + (-6)^2} = \sqrt{64 + 36} = \sqrt{100} = 10 \]

3. **Distance from (5, 12)**:
- Using the distance formula:
\[ d_3 = \sqrt{(5 - 0)^2 + (12 - 0)^2} \]
- Calculate:
\[ d_3 = \sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13 \]

4. **Distance from (7, 24)**:
- Using the distance formula:
\[ d_4 = \sqrt{(7 - 0)^2 + (24 - 0)^2} \]
- Calculate:
\[ d_4 = \sqrt{7^2 + 24^2} = \sqrt{49 + 576} = \sqrt{625} = 25 \]

### Final Results:
- Distance from (3, -4) is **5 units**.
- Distance from (-8, -6) is **10 units**.
- Distance from (5, 12) is **13 units**.
- Distance from (7, 24) is **25 units**.