https://file.aiquickdraw.com/mathbot/file/1728560253093d7xvmthq.jpg

The task asks to calculate the modulus (length) of a vector based on its coordinates in the 2D plane.

### Step-by-Step Solution:

1. **Extract Coordinates:**
   - From the graph, the vector starts at point \((-4, 1)\) and ends at \((3, 5)\).
   - So, the coordinates of the starting point are \((-4, 1)\), and the coordinates of the endpoint are \((3, 5)\).

2. **Formula for Vector Length:**
   The length (modulus) of a vector \(\vec{t}\) from point \((x_1, y_1)\) to point \((x_2, y_2)\) is given by the formula:
   \[
   |\vec{t}| = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
   \]

3. **Substitute Coordinates:**
   Substituting \((-4, 1)\) for \((x_1, y_1)\) and \((3, 5)\) for \((x_2, y_2)\):
   \[
   |\vec{t}| = \sqrt{(3 - (-4))^2 + (5 - 1)^2}
   \]
   \[
   |\vec{t}| = \sqrt{(3 + 4)^2 + (5 - 1)^2}
   \]
   \[
   |\vec{t}| = \sqrt{7^2 + 4^2}
   \]
   \[
   |\vec{t}| = \sqrt{49 + 16}
   \]
   \[
   |\vec{t}| = \sqrt{65}
   \]

4. **Round the Result:**
   - \(\sqrt{65} \approx 8.06\), and rounding it to the nearest whole number gives \(8\).

Thus, the length of the vector is approximately **8 units**.

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Do you have any questions or need further details?

### Related Questions:
1. How do you find the direction of a vector given its coordinates?
2. How do you calculate the unit vector from two points in the plane?
3. Can you calculate the distance between two points in 3D space using a similar formula?
4. How do you add or subtract vectors graphically and algebraically?
5. What is the difference between a vector's modulus and its components?

**Tip:** The modulus of a vector represents its magnitude or length, and it's always a positive value.

Koordinātu plaknē dots vektors. Nosaki šī vektora garumu! (Find the modulus or length of the vector in the 2D plane.)

Learn how to calculate the length of a vector given its coordinates in a 2D plane. Using the formula |t| = sqrt((x2 - x1)^2 + (y2 - y1)^2), this problem involves key geometry concepts like the Pythagorean theorem. Suitable for Grades 8-10.

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