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What is the distance, d, between the points (2,5/2) and (8/3,1)?

answer in the simplest radical form.

User Miao
by
8.3k points

2 Answers

5 votes

Answer: Exact Form:

97

6

Decimal Form:

1.64147630

Btw that's 97 radical 6

~ zachary

User DragonFax
by
7.8k points
6 votes

Answer:


d=(√(97))/(6)\approx1.6415

Explanation:

We have the two points: (2, 5/2) and (8/3, 1).

And we want to find the distance between them.

So, we can use the distance formula:


d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2

Let (2, 5/2) be (x₁, y₁) and let (8/3, 1) be (x₂, y₂). Substitute:


d=\sqrt{((8)/(3)-2)^2+({1-(5)/(2))^2

Evaluate the expressions within the parentheses. For the first term, we can change 2 to 6/3. For the second term, we can change 1 to 2/2. So:


d=\sqrt{((8)/(3)-(6)/(3))^2+({(2)/(2)-(5)/(2))^2

Evaluate:


d=\sqrt{((2)/(3))^2+(-(3)/(2))^2

Square:


d=\sqrt{(4)/(9)+(9)/(4)

Add. We can change 4/9 to 16/36. And we can change 9/4 to 81/36. So:


d=\sqrt{(16)/(36)+(81)/(36)}

Add:


d=\sqrt{(97)/(36)}

We can separate the square roots:


d=(√(97))/(√(36))

Simplify. So, our distance is:


d=(√(97))/(6)\approx1.6415

User NewNameStat
by
8.2k points

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