College Algebra CLEP Prep Practice Exam

What is the distance between the points (2,1) and (7,5)?

1. 6

2. 5

3. 4

4. 3

The correct answer is: 6

The distance between any two points can be calculated using the Pythagorean theorem, which states that the square of the distance between the two points is equal to the sum of the squares of the differences in their coordinates. In this case, the x-coordinates are 5 units apart (7-2=5) and the y-coordinates are 4 units apart (5-1=4). Using the Pythagorean theorem, we can find the distance to be 6 (5^2 + 4^2 = 25 + 16 = 41, and √41 ≈ 6). Option B is incorrect because it only represents the difference in the y-coordinates and does not account for the distance between the two points in the x-direction. Option C is incorrect because it represents the distance between the two points if they were aligned along the line y=x,