Question

Which points are separated by a distance of 3 units?

A. (6,3),(6,1)
B. (2,4),(2,7)
C. (3,4),(3,8)
D. (1,1),(1,2)

Answer 1

The points separated by a distance of 3 units are (2,4) and (2,7).

Step-by-step explanation:

The points that are separated by a distance of 3 units are:

1. (6,3), (6,1)
2. (2,4), (2,7)
3. (3,4), (3,8)
4. (1,1), (1,2)

To determine if the points are separated by a distance of 3 units, we can use the distance formula: d = √((x2 - x1)^2 + (y2 - y1)^2).

Calculating the distance for each pair of points:
(6,3) and (6,1): d = √((6 - 6)^2 + (3 - 1)^2) = √(0^2 + 2^2) = √4 = 2
(2,4) and (2,7): d = √((2 - 2)^2 + (4 - 7)^2) = √(0^2 + (-3)^2) = √9 = 3
(3,4) and (3,8): d = √((3 - 3)^2 + (4 - 8)^2) = √(0^2 + (-4)^2) = √16 = 4
(1,1) and (1,2): d = √((1 - 1)^2 + (1 - 2)^2) = √(0^2 + (-1)^2) = √1 = 1

Therefore, the points separated by a distance of 3 units are (2,4) and (2,7), so the answer is B.