Find the distance between the pair of points and . If necessary, express the ans
The distance between the given points is units.
(Simplify your answer. Type an exact answer, using radicals as needed.)
Express the distance rounded to two decimal places if the exact simplified answer contain
Select the correct choice below and, if necessary, fill in the answer box to complete your c
A. The distance between the given points is approximately
(Type an integer or decimal rounded to two decimal places as needed.)
B. The exact simplified form does not contain radicals.

Ask by Ingram Turner. in the United States

Mar 25,2025

Question

Find the distance between the pair of points and . If necessary, express the ans
The distance between the given points is units.
(Simplify your answer. Type an exact answer, using radicals as needed.)
Express the distance rounded to two decimal places if the exact simplified answer contain
Select the correct choice below and, if necessary, fill in the answer box to complete your c
A. The distance between the given points is approximately
(Type an integer or decimal rounded to two decimal places as needed.)
B. The exact simplified form does not contain radicals.

Ask by Ingram Turner. in the United States

Mar 25,2025

UpStudy AI · Accepted Answer

1. Compute the difference in the $$x$$-coordinates:
   $$
   8 - 3 = 5
   $$

2. Compute the difference in the $$y$$-coordinates:
   $$
   9 - 4 = 5
   $$

3. Apply the distance formula:
   $$
   \text{Distance} = \sqrt{(8-3)^2 + (9-4)^2} = \sqrt{5^2 + 5^2} = \sqrt{25 + 25} = \sqrt{50}
   $$

4. Simplify the square root:
   $$
   \sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2}
   $$

5. Thus, the exact distance between the points is:
   $$
   \boxed{5\sqrt{2}}
   $$

6. Rounded to two decimal places (using $$\sqrt{2} \approx 1.414$$):
   $$
   5 \times 1.414 \approx 7.07
   $$

The distance between the given points is approximately $$7.07$$ units.
The distance between the points $$ (3,4) $$ and $$ (8,9) $$ is $$ 5\sqrt{2} $$ units, which is approximately $$7.07$$ units.

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