To find the distance between the points (7, 8) and (-8, 0) on a coordinate grid, you can use the distance formula. The distance formula is derived from the Pythagorean theorem and is used to determine the distance between two points in a plane. The formula is:
[tex]\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
Given the points [tex]\((x_1, y_1) = (7, 8)\)[/tex] and [tex]\((x_2, y_2) = (-8, 0)\)[/tex], let's find each part of the formula step-by-step.
1. Identify coordinates:
- First point [tex]\((x_1, y_1) = (7, 8)\)[/tex]
- Second point [tex]\((x_2, y_2) = (-8, 0)\)[/tex]
2. Calculate the difference in the x-coordinates [tex]\((x_2 - x_1)\)[/tex]:
[tex]\[ -8 - 7 = -15 \][/tex]
So, the difference in the x-coordinates is [tex]\(-15\)[/tex].
3. Calculate the difference in the y-coordinates [tex]\((y_2 - y_1)\)[/tex]:
[tex]\[ 0 - 8 = -8 \][/tex]
So, the difference in the y-coordinates is [tex]\(-8\)[/tex].
4. Square the differences:
[tex]\[ (-15)^2 = 225 \][/tex]
[tex]\[ (-8)^2 = 64 \][/tex]
5. Sum the squared differences:
[tex]\[ 225 + 64 = 289 \][/tex]
6. Take the square root of the sum:
[tex]\[ \sqrt{289} = 17 \][/tex]
Therefore, the distance between the points (7, 8) and (-8, 0) on a coordinate grid is [tex]\(17.0\)[/tex] units.
