Question

find the distance, d, of \\(\overline{ab}\\).
\\(a = (12, 4)\\) \\(b = (0, 11)\\)

\\(d = ?\\)

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

round to the nearest tenth.

Explanation:

Identify coordinates

We have points \(A(12, 4)\) and \(B(0, 11)\).
Let \((x_1, y_1) = (12, 4)\) and \((x_2, y_2) = (0, 11)\).

Apply distance formula

Use the given distance formula:

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

Substitute values

Substitute the coordinates into the formula:

$$d = \sqrt{(0 - 12)^2 + (11 - 4)^2}$$

Simplify terms

Calculate the differences and their squares:

$$d = \sqrt{(-12)^2 + (7)^2}$$

$$d = \sqrt{144 + 49}$$

$$d = \sqrt{193}$$

Round to nearest tenth

Calculate the square root value:

$$d \approx 13.892$$

Rounding to the nearest tenth gives:

$$d \approx 13.9$$

Answer:

Find the distance, d, of \(\overline{AB}\).
\(A = (12, 4)\) \(B = (0, 11)\)
\(d =\) <blank>\(13.9\)</blank>
Round to the nearest tenth