Question

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

Answer 1

Answer: Exact Form:

√

97

6

Decimal Form:

1.64147630

Btw that's 97 radical 6

~ zachary

Answer 2

Answer:

$d=\frac{\sqrt{97}}{6}\approx1.6415$

Step-by-step 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:

$d=\sqrt{(\frac{8}{3}-2)^2+({1-\frac{5}{2})^2$

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:

$d=\sqrt{(\frac{8}{3}-\frac{6}{3})^2+({\frac{2}{2}-\frac{5}{2})^2$

Evaluate:

$d=\sqrt{(\frac{2}{3})^2+(-\frac{3}{2})^2$

Square:

$d=\sqrt{\frac{4}{9}+\frac{9}{4}$

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

$d=\sqrt{\frac{16}{36}+\frac{81}{36}}$

Add:

$d=\sqrt{\frac{97}{36}}$

We can separate the square roots:

$d=\frac{\sqrt{97}}{\sqrt{36}}$

Simplify. So, our distance is:

$d=\frac{\sqrt{97}}{6}\approx1.6415$