XI, Find the distance between the points \( (2,-5) \) and \( (10,-5) \) \( \square \) units

To find the distance between the points \( (2,-5) \) and \( (10,-5) \), you can use the distance formula. However, since both points have the same y-coordinate, the distance is simply the difference in their x-coordinates. The calculation is: \[ Distance = |x_2 - x_1| = |10 - 2| = 8 \] So, the distance between the points is \( 8 \) units. In terms of geometry, when two points lie on the same horizontal line (having equal y-coordinates), their distance can be visualized simply as the length of a horizontal line segment between them. It's a straightforward way to understand this concept practically! Interesting fact: Historically, the concept of distance has been crucial in many fields such as surveying, navigation, and architecture. Ancient civilizations like the Egyptians and Romans used rudimentary tools to calculate distance for building projects and road systems that laid the foundation for modern engineering!