What is the length of a segment whose endpoints are (5, -8) and (9,2). Please explain to me what the formula or rules for working this problem.
think of the line segment as the hypotenuse of a right triangle. Then the legs have length (9-5)=4 and (2-(-8))=10.
So the length of the line segment is sqrt(4^2 + 10^2) = 10.77
To find the length of a segment using the coordinates of its endpoints, you can use the distance formula. The distance formula is derived from the Pythagorean theorem and calculates the distance between two points in a coordinate plane.
Here are the steps to follow:
1. Identify the coordinates of the endpoints: In this case, the endpoints are (5, -8) and (9, 2).
2. Use the distance formula: The distance formula is given by the equation:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
Here, (x₁, y₁) are the coordinates of the first endpoint, and (x₂, y₂) are the coordinates of the second endpoint.
3. Substitute the coordinates into the formula: For our example, let's use (5, -8) as the first endpoint and (9, 2) as the second endpoint.
d = √((9 - 5)² + (2 - (-8))²)
= √(4² + 10²)
= √(16 + 100)
= √116
≈ 10.77 (rounded to two decimal places)
Therefore, the length of the segment with endpoints (5, -8) and (9, 2) is approximately 10.77 units.