The length of the segment joining the points with coordinates (-2,4) and (3,-5) is

Options

A. 2.8
B. 3.7
C. 10
D. 10.3

Explanation

To find the length of the segment joining the points with coordinates (-2, 4) and (3, -5), we will use the distance formula. The distance formula is given by:

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

where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the two points.

### Step-by-step Solution:

1. **Identify the coordinates:**
- Let point P be \((-2, 4)\) which means \(x_1 = -2\) and \(y_1 = 4\).
- Let point Q be \((3, -5)\) which means \(x_2 = 3\) and \(y_2 = -5\).

2. **Substitute the coordinates into the distance formula:**
\[ d = \sqrt{(3 - (-2))^2 + (-5 - 4)^2} \]

3. **Simplify the expressions inside the parentheses:**
- Calculate \(x_2 - x_1\):
\[ 3 - (-2) = 3 + 2 = 5 \]
- Calculate \(y_2 - y_1\):
\[ -5 - 4 = -9 \]

4. **Plug these values back into the formula:**
\[ d = \sqrt{(5)^2 + (-9)^2} \]

5. **Calculate the squares:**
- \(5^2 = 25\)
- \((-9)^2 = 81\)

6. **Add the squares:**
\[ d = \sqrt{25 + 81} = \sqrt{106} \]

7. **Approximate the square root:**
\[ d \approx 10.3 \]

### Final Answer:
The length of the segment joining the points (-2, 4) and (3, -5) is approximately \(10.3\).

---