Question

What is the distance between b and c?

Answer 1

`c = √(74)`

Explanation:

To find the distance between the two, we will use the Pythagorean theorem (
`a^(2) + b^(2) = c^(2)`). To find a and b, we need to subtract the distances between the y coordinates and the x coordinates respectively. For the x coordinates, we have 8 - 1 = 7 units. For the y coordinates, we have 7 - 2 = 5. Plugging this into our equation gives us:

`7^(2) + 5^(2) = c^(2)`

We will simplify our exponents:

`49 + 25 = c^(2)`

Then adding them together gives us:

`74 = c^(2)`

Then, we square root both sides giving us:

`√(74) = c`

Then, we cannot simplify past this, since 74's prime factorization doesn't allow it. So,
`c = √(74)`.

Hope this helped!