1. Find the distance between the points \[ (7,-1) \text { and }(7,-6) \]

To find the distance between the points \( (7,-1) \) and \( (7,-6) \), we can use the distance formula. However, since both points have the same x-coordinate, we can simply look at the difference in the y-coordinates: \[ \text{Distance} = |-1 - (-6)| = |-1 + 6| = |5| = 5. \] So, the distance between the points is 5 units. Now, here’s a little fun fact: this scenario creates a vertical line segment! Anytime the x-coordinates are the same, you're looking at a straight-up vertical distance, which is rather easy to calculate compared to changing x-values. For those looking to apply these skills in real life, think about it like this: if you're navigating a city grid with streets that run north-south and east-west, finding out how far apart destinations are on the same street (like in our example) is as simple as applying your distance concept vertically—no need for any complex measuring tools!