The distance between the points (2,4) and (6,-5) is calculated using the distance formula, resulting in √((6-2)^2 + (-5-4)^2) which simplifies to √97. Thus, the correct answer is D, √97.
The distance between two points can be calculated using the distance formula, which is derived from the Pythagorean theorem.
The formula is √((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) and (x2, y2) are the coordinates of the two points.
In your case, the points provided are (2,4) and (6,-5). Using the distance formula:
Calculate the difference in the x-coordinates: 6 - 2 = 4
Calculate the difference in the y-coordinates: -5 - 4 = -9
Square both differences: 4^2 = 16 and (-9)^2 = 81
Add the squares: 16 + 81 = 97
Take the square root of the sum: √97
Therefore, the distance between the points (2,4) and (6,-5) is √97, which corresponds to answer choice D.
The probable question may be:
Khan academy what is the distance between two points?
first point is (2,4) and second point is (6,-5)
A. 12
B. 13
C. \sqrt{36}
D. \sqrt{97}