The coordinates of the endpoints of AB¯¯¯¯¯ and CD¯¯¯¯¯ are A(2, 3), B(8, 1), C(5, 2), and D(6, 5). Which statement about the line segments is true?
It would help to have the statements ...
To determine which statement about the line segments AB¯¯¯¯¯ and CD¯¯¯¯¯ is true, we need to analyze their characteristics. Here are the steps to do it:
1. Find the lengths of each line segment:
- The length of AB¯¯¯¯¯ can be calculated using the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
d_AB = √((8 - 2)^2 + (1 - 3)^2) = √((6)^2 + (-2)^2) = √(36 + 4) = √40 = 2√10
- The length of CD¯¯¯¯¯ can be calculated similarly:
d_CD = √((6 - 5)^2 + (5 - 2)^2) = √((1)^2 + (3)^2) = √(1 + 9) = √10
2. Compare the lengths of the line segments:
- The length of AB¯¯¯¯¯ is 2√10.
- The length of CD¯¯¯¯¯ is √10.
Based on these calculations, we can conclude that the statement "AB¯¯¯¯¯ is longer than CD¯¯¯¯¯" is true.