To determine the distance between the points [tex]\((-2, -8)\)[/tex] and [tex]\((1, 2)\)[/tex], we can use the distance formula. The distance formula is derived from the Pythagorean theorem and is given by:
[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
Here, [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] are the coordinates of the two points. Let's plug in the given coordinates:
1. Identify the coordinates of the points:
- Point 1: [tex]\((x_1, y_1) = (-2, -8)\)[/tex]
- Point 2: [tex]\((x_2, y_2) = (1, 2)\)[/tex]
2. Substitute the coordinates into the distance formula:
[tex]\[ d = \sqrt{(1 - (-2))^2 + (2 - (-8))^2} \][/tex]
3. Simplify the expressions inside the parentheses:
[tex]\[ d = \sqrt{(1 + 2)^2 + (2 + 8)^2} \][/tex]
[tex]\[ d = \sqrt{3^2 + 10^2} \][/tex]
4. Square the values:
[tex]\[ d = \sqrt{9 + 100} \][/tex]
5. Add the squared values:
[tex]\[ d = \sqrt{109} \][/tex]
6. Take the square root of 109:
[tex]\[ d \approx 10.44030650891055 \][/tex]
So, the distance between the points [tex]\((-2, -8)\)[/tex] and [tex]\((1, 2)\)[/tex] is approximately [tex]\(10.44\)[/tex].
