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Given the points [tex]$(-3, 8)$[/tex] and [tex]$(2, 4)$[/tex], solve for the distance between the points.

Sagot :

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].