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In Mathematics / High School | 2014-04-27

What is the length of the line segment in the x-y plane with endpoints at (-2, -2) and (2, 3)?

Can anyone explain how to find this step by step?

Asked by Conway193

Answer (3)

You've got a formula. If the two endpoints are A ( x A ​ , y A ​ ) and A ( x B ​ , y B ​ ) , then the length is ( x B ​ − x A ​ ) 2 + ( y B ​ − y A ​ ) 2 ​ . The result is 16 + 25 ​ = 41 ​ .

Answered by Anonymous | 2024-06-10

To calculate the length of a line segment in the x-y plane with endpoints at (-2,-2) and (2,3), we use the distance formula derived from the Pythagorean theorem, which is: Distance = √((x2 - x1)² + (y2 - y1)²). Here, (x1, y1) and (x2, y2) are the coordinates of the two endpoints of the line segment.
Step by step calculation:
First, identify the coordinates of the two points. Point 1: (-2, -2), Point 2: (2, 3).
Apply the distance formula: √((2 - (-2))² + (3 - (-2))²).
Simplify the expression inside the square root: √((4)² + (5)²).
Square each difference: √(16 + 25).
Sum the squares: √(41).
Lastly, take the square root to find the distance: √(41) or approximately 6.40 units.
Therefore, the length of the line segment is √(41) units, or approximately 6.40 units.

Answered by BenicioBrody | 2024-06-24

The length of the line segment with endpoints at (-2, -2) and (2, 3) is calculated using the distance formula, resulting in 41 ​ units, or approximately 6.40 units.
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Answered by BenicioBrody | 2025-01-12

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