point A is located at (1,5) and point B is located at (3,2). What is the length of line segment AB in simplest radical form
c^2 = a^2+b^2
= (3-1)^2 + (5-3)^2
= 2^2 + 2^2
= 4+4
= 8
c = √8
= √(4*2)
= √4*√2
= 2√2
To find the length of line segment AB, we can use the distance formula. The distance between two points (x₁, y₁) and (x₂, y₂) can be calculated using the formula:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
In this case, point A is located at (1, 5) and point B is located at (3, 2). Plugging these values into the formula, we get:
d = √((3 - 1)² + (2 - 5)²)
= √(2² + (-3)²)
= √(4 + 9)
= √13
Therefore, the length of line segment AB is √13 in simplest radical form.