To find the distance between two points, we can use the distance formula, which is defined as:
[tex]\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
We are given the coordinates of point A as (0, 4) and the coordinates of point B as (-2, -7). Let [tex]\( (x_1, y_1) \)[/tex] be the coordinates of point A and [tex]\( (x_2, y_2) \)[/tex] be the coordinates of point B.
1. Identify the coordinates:
- Point A: [tex]\( (x_1, y_1) = (0, 4) \)[/tex]
- Point B: [tex]\( (x_2, y_2) = (-2, -7) \)[/tex]
2. Substitute the coordinates into the distance formula:
[tex]\[ \text{Distance} = \sqrt{((-2) - 0)^2 + ((-7) - 4)^2} \][/tex]
3. Simplify inside the square root:
[tex]\[ \text{Distance} = \sqrt{(-2 - 0)^2 + (-7 - 4)^2} \][/tex]
[tex]\[ \text{Distance} = \sqrt{(-2)^2 + (-11)^2} \][/tex]
4. Calculate the squares:
[tex]\[ \text{Distance} = \sqrt{4 + 121} \][/tex]
[tex]\[ \text{Distance} = \sqrt{125} \][/tex]
5. Find the square root of 125:
[tex]\[ \text{Distance} \approx 11.180339887498949 \][/tex]
6. Round the distance to the nearest tenth:
[tex]\[ \text{Distance (rounded)} = 11.2 \][/tex]
So the distance between point A and point B, rounded to the nearest tenth, is
[tex]\[ 11.2 \][/tex]
Thus, the correct answer is:
- 11.2
