Question

pythagorean distance
what is the distance c?
pythagorean formula \\( c^2 = a^2 + b^2 \\)
(the image contains a coordinate grid with two blue dots, labeled a=4 (horizontal distance), b=1 (vertical distance), and c as the hypotenuse to find. on the right, there are number and square root options.)

Explanation:

Step1: Identify values of a and b

From the graph, \(a = 4\) and \(b = 1\).

Step2: Apply Pythagorean formula

The Pythagorean formula is \(c^{2}=a^{2}+b^{2}\). Substitute \(a = 4\) and \(b = 1\) into the formula:

$$
LATEXBLOCK0
$$

Step3: Solve for c

Take the square root of both sides: \(c=\sqrt{17}\) (since distance is positive).

Answer:

\(\sqrt{17}\) (or approximately \(4.1\))