Final answer:
The distance between the points (10,9) and (2,–6) is found by using the Pythagorean theorem on the differences in their x and y coordinates, resulting in a distance of 17 units.
Step-by-step explanation:
To find the distance between the points (10,9) and (2,–6), we can use the Pythagorean theorem. This theorem states that in a right triangle, the sum of the squares of the two legs (a and b) is equal to the square of the hypotenuse (c).
In this case, the difference in the x-coordinates (10 - 2) is 8, and the difference in the y-coordinates (9 - (-6)) is 15, which represent the two legs of a right triangle.
Applying the Pythagorean theorem:
a² + b² = c²
8² + 15² = c²
64 + 225 = c²
289 = c²
c = √289
c = 17
Therefore, the distance between the points (10,9) and (2,–6) is 17 units.