What is the length of vector (-6, 8)?

The length of the vector (-6, 8) is 10 units.

To find the length of a vector, we use the Pythagorean theorem. The vector (-6, 8) can be thought of as a right-angled triangle with sides of lengths 6 and 8. The length of the vector is the hypotenuse of this triangle. According to the Pythagorean theorem, the length (or magnitude) of the vector is given by the square root of the sum of the squares of its components.

Mathematically, this is written as:
\[ \text{Length} = \sqrt{(-6)^2 + 8^2} \]

First, we square each component:
\[ (-6)^2 = 36 \]
\[ 8^2 = 64 \]

Next, we add these squares together:
\[ 36 + 64 = 100 \]

Finally, we take the square root of the sum:
\[ \sqrt{100} = 10 \]

Therefore, the length of the vector (-6, 8) is 10 units. This method can be applied to any vector in two dimensions to find its length. Remember, the components of the vector are simply the differences in the x and y coordinates from the origin to the point represented by the vector.