Find the distance between the origin and the point :
(8, -15)

Answer

To find the distance between the origin (0, 0) and the point (8, -15), we will use the distance formula. The distance formula states that the distance \( d \) between two points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) is given by:

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

### Step 1: Identify the coordinates
Let point A be the origin (0, 0), so \( x_1 = 0 \) and \( y_1 = 0 \). Let point B be (8, -15), so \( x_2 = 8 \) and \( y_2 = -15 \).

### Step 2: Substitute the coordinates into the distance formula
Now we can substitute these values into the distance formula:

\[ d = \sqrt{(8 - 0)^2 + (-15 - 0)^2} \]

### Step 3: Simplify the expression
Calculating the differences:

\[ d = \sqrt{(8)^2 + (-15)^2} \]

Calculating the squares:

\[ d = \sqrt{64 + 225} \]

### Step 4: Add the squared values
Now, add the squared values:

\[ d = \sqrt{289} \]

### Step 5: Calculate the square root
Finally, calculate the square root:

\[ d = 17 \]

### Conclusion
Thus, the distance between the origin and the point (8, -15) is **17 units**.

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