Sure, let's solve this step-by-step.
Firstly, we need to find the Euclidean distance between the two given points, [tex]\((-3, 8)\)[/tex] and [tex]\((2, 4)\)[/tex].
The formula to calculate the Euclidean distance between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[
\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\][/tex]
Let's identify the coordinates from the points:
- For point [tex]\((-3, 8)\)[/tex], we have [tex]\(x_1 = -3\)[/tex] and [tex]\(y_1 = 8\)[/tex].
- For point [tex]\((2, 4)\)[/tex], we have [tex]\(x_2 = 2\)[/tex] and [tex]\(y_2 = 4\)[/tex].
Next, we substitute these coordinates into the distance formula:
1. Calculate [tex]\(x_2 - x_1\)[/tex]:
[tex]\[
x_2 - x_1 = 2 - (-3) = 2 + 3 = 5
\][/tex]
2. Calculate [tex]\(y_2 - y_1\)[/tex]:
[tex]\[
y_2 - y_1 = 4 - 8 = -4
\][/tex]
3. Square the differences calculated in steps 1 and 2:
[tex]\[
(x_2 - x_1)^2 = 5^2 = 25
\][/tex]
[tex]\[
(y_2 - y_1)^2 = (-4)^2 = 16
\][/tex]
4. Sum up the squared differences:
[tex]\[
(x_2 - x_1)^2 + (y_2 - y_1)^2 = 25 + 16 = 41
\][/tex]
5. Take the square root of the sum obtained in step 4 to find the distance:
[tex]\[
\text{Distance} = \sqrt{41} \approx 6.4031242374328485
\][/tex]
Thus, the Euclidean distance between the points [tex]\((-3, 8)\)[/tex] and [tex]\((2, 4)\)[/tex] is approximately [tex]\(6.4031242374328485\)[/tex].
