Find the distance between the following pairs of points
(0,0),(-4,3)

Answer

To find the distance between the points (0,0) and (-4,3), 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 the points be:
- Point A: \( (x_1, y_1) = (0, 0) \)
- Point B: \( (x_2, y_2) = (-4, 3) \)

### Step 2: Substitute the coordinates into the distance formula
Now, we substitute the coordinates into the distance formula:

\[ d = \sqrt{((-4) - 0)^2 + (3 - 0)^2} \]

### Step 3: Simplify the expression
Calculating the differences:
- For \(x\): \((-4) - 0 = -4\)
- For \(y\): \(3 - 0 = 3\)

Now substitute these values back into the formula:

\[ d = \sqrt{(-4)^2 + (3)^2} \]

### Step 4: Calculate the squares
Now calculate the squares:

\[ d = \sqrt{16 + 9} \]

### Step 5: Add the squares
Adding the squares gives:

\[ d = \sqrt{25} \]

### Step 6: Take the square root
Finally, take the square root:

\[ d = 5 \]

Thus, the distance between the points (0,0) and (-4,3) is **5**.

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