The text in the image reads:

"Длина вектора, соединяющего точки $A(2, 3)$ и $B(10, -3)$, равна ..."

This translates to:

"The length of the vector connecting points $A(2, 3)$ and $B(10, -3)$ is equal to ..."

To find the length of the vector, we use the distance formula:

$\text{Length} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Step-by-step Solution:

1. Points:

   • $A(2, 3)$: $x_1 = 2, y_1 = 3$
   • $B(10, -3)$: $x_2 = 10, y_2 = -3$

2. Substitute into the formula: $\text{Length} = \sqrt{(10 - 2)^2 + (-3 - 3)^2}$

3. Simplify the differences: $\text{Length} = \sqrt{(8)^2 + (-6)^2}$

4. Square the differences: $\text{Length} = \sqrt{64 + 36}$

5. Add: $\text{Length} = \sqrt{100}$

6. Simplify: $\text{Length} = 10$

Final Answer:

The length of the vector is 10.

Would you like additional explanation or details?

Here are 5 related questions:

1. How do you find the midpoint of a line segment connecting two points?
2. What is the formula for the slope of the line connecting two points?
3. How do you represent a vector in component form?
4. What does the magnitude of a vector represent geometrically?
5. Can vectors in three-dimensional space also be measured using a similar distance formula?

Tip: When dealing with vector length, always ensure both points are correctly substituted into the distance formula.