Question

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

answer in the simplest radical form.

Answer 1

Answer: Exact Form:

√

97

6

Decimal Form:

1.64147630

Btw that's 97 radical 6

~ zachary

Answer 2

`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`