What is the distance between (-4,5) (1,17)

The distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) in a plane is given by the distance formula:

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

For the points \((-4, 5)\) and \((1, 17)\):

\[
d = \sqrt{{(1 - (-4))}^2 + {(17 - 5)}^2}
\]

Simplify the expression:

\[
d = \sqrt{{(1 + 4)}^2 + {(17 - 5)}^2} = \sqrt{{5}^2 + {12}^2}
\]

\[
d = \sqrt{25 + 144} = \sqrt{169} = 13
\]

Thus, the distance between the points is \(13\) units.

Would you like further details or have any questions?

Here are 5 related questions:
1. How would you find the midpoint between these two points?
2. What is the slope of the line connecting the two points?
3. Can you use the distance formula in 3D space?
4. How would you apply the Pythagorean theorem to this distance problem?
5. Can you derive the equation of a circle passing through these points?

**Tip:** When calculating distances, always ensure you've applied the correct signs for subtraction and carefully handle any negatives!

What is the distance between (-4,5) (1,17)?

Learn how to find the distance between points (-4, 5) and (1, 17) using the distance formula. This problem demonstrates key concepts in coordinate geometry and applies the Pythagorean theorem to calculate the distance, suitable for Grades 7-9.

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