Answer:
[tex]d=\frac{\sqrt{97}}{6}\approx1.6415[/tex]
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:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]
Let (2, 5/2) be (x₁, y₁) and let (8/3, 1) be (x₂, y₂). Substitute:
[tex]d=\sqrt{(\frac{8}{3}-2)^2+({1-\frac{5}{2})^2[/tex]
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:
[tex]d=\sqrt{(\frac{8}{3}-\frac{6}{3})^2+({\frac{2}{2}-\frac{5}{2})^2[/tex]
Evaluate:
[tex]d=\sqrt{(\frac{2}{3})^2+(-\frac{3}{2})^2[/tex]
Square:
[tex]d=\sqrt{\frac{4}{9}+\frac{9}{4}[/tex]
Add. We can change 4/9 to 16/36. And we can change 9/4 to 81/36. So:
[tex]d=\sqrt{\frac{16}{36}+\frac{81}{36}}[/tex]
Add:
[tex]d=\sqrt{\frac{97}{36}}[/tex]
We can separate the square roots:
[tex]d=\frac{\sqrt{97}}{\sqrt{36}}[/tex]
Simplify. So, our distance is:
[tex]d=\frac{\sqrt{97}}{6}\approx1.6415[/tex]
