2 Find the distance between: a $$ \mathrm{P}(4,0) $$ and $$ \mathrm{Q}(0,-3) $$

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UpStudy AI · Accepted Answer

To find the distance between two points $$ P(4, 0) $$ and $$ Q(0, -3) $$ in a Cartesian plane, you can use the **Distance Formula**. The formula is derived from the Pythagorean theorem and is given by:

$$
\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
$$

Where:
- $$ (x_1, y_1) $$ are the coordinates of point $$ P $$.
- $$ (x_2, y_2) $$ are the coordinates of point $$ Q $$.

### Step-by-Step Calculation:

1. **Identify the coordinates:**
   - Point $$ P $$ has coordinates $$ (4, 0) $$, so $$ x_1 = 4 $$ and $$ y_1 = 0 $$.
   - Point $$ Q $$ has coordinates $$ (0, -3) $$, so $$ x_2 = 0 $$ and $$ y_2 = -3 $$.

2. **Plug the values into the Distance Formula:**

$$
\text{Distance} = \sqrt{(0 - 4)^2 + (-3 - 0)^2}
$$

3. **Calculate the differences:**
   - $$ x_2 - x_1 = 0 - 4 = -4 $$
   - $$ y_2 - y_1 = -3 - 0 = -3 $$

4. **Square the differences:**
   - $$ (-4)^2 = 16 $$
   - $$ (-3)^2 = 9 $$

5. **Add the squared differences:**
   
$$
16 + 9 = 25
$$

6. **Take the square root of the sum:**

$$
\sqrt{25} = 5
$$

### **Answer:**
The distance between points $$ P(4, 0) $$ and $$ Q(0, -3) $$ is **5 units**.
The distance between $$ P(4,0) $$ and $$ Q(0,-3) $$ is 5 units.

2 Find the distance between: a \( \mathrm{P}(4,0) \) and \( \mathrm{Q}(0,-3) \)

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