What is the distance between the points (4, -1) and (4, 6)?

What is the distance between the points (4, -1) and (4, 6)?

• A. 5
• B. 7
• C. 9
• D. 11

Answer: (B)

When two points share the same x-coordinate, the distance between them is just the vertical distance between their y-values. Here the x-values are both 4, so we look at the y-values -1 and 6. The difference is 6 minus (-1), which is 7. The distance is the absolute value of that difference: |6 - (-1)| = 7. You can also see this with the distance formula: sqrt((4-4)^2 + (6 - (-1))^2) = sqrt(0 + 7^2) = sqrt(49) = 7. So the distance is 7.

When two points share the same x-coordinate, the distance between them is just the vertical distance between their y-values. Here the x-values are both 4, so we look at the y-values -1 and 6. The difference is 6 minus (-1), which is 7. The distance is the absolute value of that difference: |6 - (-1)| = 7. You can also see this with the distance formula: sqrt((4-4)^2 + (6 - (-1))^2) = sqrt(0 + 7^2) = sqrt(49) = 7. So the distance is 7.