To determine the distance between two points on a coordinate grid, we can use the distance formula, which is derived from the Pythagorean theorem. Given two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex], the distance [tex]\(d\)[/tex] between them is given by:
[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
Let's apply this formula to the given points [tex]\((7, 8)\)[/tex] and [tex]\((-8, 0)\)[/tex]:
1. Identify the coordinates:
- Point 1: [tex]\((x_1, y_1) = (7, 8)\)[/tex]
- Point 2: [tex]\((x_2, y_2) = (-8, 0)\)[/tex]
2. Calculate the differences in coordinates:
- Difference in x-coordinates: [tex]\( dx = x_2 - x_1 = -8 - 7 = -15 \)[/tex]
- Difference in y-coordinates: [tex]\( dy = y_2 - y_1 = 0 - 8 = -8 \)[/tex]
3. Plug the differences into the distance formula:
- [tex]\( d = \sqrt{(-15)^2 + (-8)^2} \)[/tex]
- [tex]\( d = \sqrt{225 + 64} \)[/tex]
- [tex]\( d = \sqrt{289} \)[/tex]
- [tex]\( d = 17.0 \)[/tex]
Therefore, the distance between the points [tex]\((7, 8)\)[/tex] and [tex]\((-8, 0)\)[/tex] is [tex]\( 17.0 \)[/tex] units.
