To find the distance [tex]\(d\)[/tex] between points [tex]\(A = (-3, 4)\)[/tex] and [tex]\(B = (5, 8)\)[/tex], we can use the distance formula, which is given by:
[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
Let's break this down step-by-step:
1. Identify the coordinates:
- Point [tex]\(A\)[/tex] has coordinates [tex]\((x_1, y_1) = (-3, 4)\)[/tex].
- Point [tex]\(B\)[/tex] has coordinates [tex]\((x_2, y_2) = (5, 8)\)[/tex].
2. Calculate the differences:
- [tex]\( \Delta x = x_2 - x_1 = 5 - (-3) = 5 + 3 = 8 \)[/tex]
- [tex]\( \Delta y = y_2 - y_1 = 8 - 4 = 4 \)[/tex]
3. Square the differences:
- [tex]\( \Delta x^2 = 8^2 = 64 \)[/tex]
- [tex]\( \Delta y^2 = 4^2 = 16 \)[/tex]
4. Sum the squared differences:
- Sum = [tex]\( \Delta x^2 + \Delta y^2 = 64 + 16 = 80 \)[/tex]
5. Take the square root of the sum:
- [tex]\( d = \sqrt{80} \approx 8.94427190999916 \)[/tex]
6. Round to the nearest tenth:
- [tex]\( d \approx 8.9 \)[/tex]
Thus, the distance [tex]\(d\)[/tex] between points [tex]\(A\)[/tex] and [tex]\(B\)[/tex], rounded to the nearest tenth, is:
[tex]\[ d \approx 8.9 \][/tex]
