Question

pythagorean distance
what is the distance c?
pythagorean formula \\( c^2 = a^2 + b^2 \\)
(image shows a grid with two points, a=4 (horizontal distance), b=3 (vertical distance), asking for c (hypotenuse). right side has number and square root options.)

Explanation:

Step1: Identify values of a and b

From the graph, \( a = 4 \) and \( b = 3 \).

Step2: Apply Pythagorean formula

The Pythagorean formula is \( c^{2}=a^{2}+b^{2} \). Substitute \( a = 4 \) and \( b = 3 \) into the formula:

$$ c^{2}=4^{2}+3^{2}=16 + 9=25 $$

Step3: Solve for c

Take the square root of both sides: \( c=\sqrt{25} = 5 \).

Answer:

5