To determine the distance between the points [tex]\((-6, -5)\)[/tex] and [tex]\((2, 0)\)[/tex], we will use the distance formula. This formula allows us to find the distance between two points in a plane 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 coordinates of our specific points:
- [tex]\((x_1, y_1) = (-6, -5)\)[/tex]
- [tex]\((x_2, y_2) = (2, 0)\)[/tex]
Step-by-step calculation:
1. Find the difference in the x-coordinates:
[tex]\[ x_2 - x_1 = 2 - (-6) = 2 + 6 = 8 \][/tex]
2. Find the difference in the y-coordinates:
[tex]\[ y_2 - y_1 = 0 - (-5) = 0 + 5 = 5 \][/tex]
3. Square the differences:
[tex]\[ (x_2 - x_1)^2 = 8^2 = 64 \][/tex]
[tex]\[ (y_2 - y_1)^2 = 5^2 = 25 \][/tex]
4. Add the squared differences:
[tex]\[ (x_2 - x_1)^2 + (y_2 - y_1)^2 = 64 + 25 = 89 \][/tex]
5. Take the square root of the sum:
[tex]\[ d = \sqrt{89} \approx 9.434 \][/tex]
Thus, the distance between the points [tex]\((-6, -5)\)[/tex] and [tex]\((2, 0)\)[/tex] is approximately [tex]\(9.434\)[/tex].
So, the final solution yields:
- The distance is [tex]\(9.434\)[/tex].
- The coordinates of the two points are [tex]\((-6, -5)\)[/tex] and [tex]\((2, 0)\)[/tex].
