Final answer:
The distance between the points (2, 10) and (-4, 2) is determined by calculating the square root of the sum of the squares of the differences in the x and y coordinates, which equals 10 units.
Step-by-step explanation:
The distance between the points (2, 10) and (-4, 2) on the coordinate plane can be calculated using the distance formula which is derived from the Pythagorean theorem. To find the distance, we use the formula √((x2-x1)² + (y2-y1)²), where (x1, y1) and (x2, y2) are the coordinates of the two points.
In this case, we have:
x1 = 2, y1 = 10
x2 = -4, y2 = 2
The calculation is as follows:
Distance = √((-4-2)² + (2-10)²) = √(((-6)²) + ((-8)²)) = √(36 + 64) = √100 = 10
So, the distance between the two points is 10 units, which corresponds to option D).