What is the distance of 4/5 of the points -1,2 and 4,8

To find the distance between two points \( A(-1, 2) \) and \( B(4, 8) \), we first calculate the full distance using the distance formula:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Substituting the coordinates:

\[
d = \sqrt{(4 - (-1))^2 + (8 - 2)^2}
\]

Simplifying:

\[
d = \sqrt{(4 + 1)^2 + (8 - 2)^2} = \sqrt{5^2 + 6^2} = \sqrt{25 + 36} = \sqrt{61}
\]

The full distance between the points is \( \sqrt{61} \).

Next, to find \( \frac{4}{5} \) of this distance:

\[
\text{Distance} = \frac{4}{5} \times \sqrt{61}
\]

Thus, the distance is:

\[
\boxed{\frac{4\sqrt{61}}{5}}
\]

Would you like to know more details or have any questions about this calculation?

Here are 5 related questions you might find interesting:

1. What is the exact decimal value of \( \sqrt{61} \)?
2. How do you find the coordinates of a point that is \( \frac{4}{5} \) of the way from \( A \) to \( B \)?
3. What is the slope of the line passing through the points \( (-1, 2) \) and \( (4, 8) \)?
4. How would the distance change if the points were \( (-1, -2) \) and \( (4, -8) \)?
5. What is the midpoint of the segment connecting \( A(-1, 2) \) and \( B(4, 8) \)?

**Tip:** When solving distance-related problems, double-check the sign operations when subtracting coordinates to avoid errors.

Learn how to calculate 4/5 of the distance between two points (-1, 2) and (4, 8) using the distance formula. This problem explores fractional distances and includes step-by-step calculations. Suitable for high school students.

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