For points (1,2) and (4,7), the distance is:

For points (1,2) and (4,7), the distance is:

• A. 6
• B. 5
• C. sqrt(34)
• D. sqrt(50)

Answer: (C)

The distance between two points in the plane is the length of the straight line connecting them, found with the distance formula: distance = sqrt[(x2 − x1)^2 + (y2 − y1)^2]. Here the differences are 4 − 1 = 3 and 7 − 2 = 5. So the distance is sqrt(3^2 + 5^2) = sqrt(9 + 25) = sqrt(34). Since 34 isn’t a perfect square, it stays as sqrt(34). This is the length of the hypotenuse of a right triangle with legs 3 and 5, which is exactly the straight-line distance between the two points.

The distance between two points in the plane is the length of the straight line connecting them, found with the distance formula: distance = sqrt[(x2 − x1)^2 + (y2 − y1)^2]. Here the differences are 4 − 1 = 3 and 7 − 2 = 5. So the distance is sqrt(3^2 + 5^2) = sqrt(9 + 25) = sqrt(34). Since 34 isn’t a perfect square, it stays as sqrt(34). This is the length of the hypotenuse of a right triangle with legs 3 and 5, which is exactly the straight-line distance between the two points.