Kanan was asked to graph point J ( −4, −6) and point K (4, 4) on a coordinate grid.



To the nearest whole number, what measurement is the closest to the distance between point J and point K in units?

________ units


To find the distance between two points on a coordinate plane, we use the distance formula:

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

Where:
- \( (x_1, y_1) \) is point J, which is \( (-4, -6) \)
- \( (x_2, y_2) \) is point K, which is \( (4, 4) \)

Now, substitute the coordinates into the formula:

\[
d = \sqrt{(4 - (-4))^2 + (4 - (-6))^2}
\]
\[
d = \sqrt{(4 + 4)^2 + (4 + 6)^2}
\]
\[
d = \sqrt{8^2 + 10^2}
\]
\[
d = \sqrt{64 + 100}
\]
\[
d = \sqrt{164}
\]
\[
d \approx 12.81
\]

To the nearest whole number, the distance between point J and point K is **13 units**.

Would you like further details or have any questions?

---

Here are 5 follow-up questions:
1. How would the distance formula change if one of the points had negative coordinates?
2. Can you derive the distance formula from the Pythagorean theorem?
3. How do you plot the points \( (-4, -6) \) and \( (4, 4) \) on a graph?
4. What are the coordinates of a point that is halfway between point J and point K?
5. How does the distance change if you move both points closer together by 2 units?

**Tip:** The distance formula is a direct application of the Pythagorean theorem, which applies in two-dimensional space to find the length of the hypotenuse of a right triangle.

Kanan was asked to graph point J (−4, −6) and point K (4, 4) on a coordinate grid. To the nearest whole number, what measurement is the closest to the distance between point J and point K in units?

Find the distance between points J(-4, -6) and K(4, 4) using the distance formula. This problem involves coordinate geometry and applies the Pythagorean theorem to calculate the distance to the nearest whole number, which is 13 units. Suitable for students in Grades 8-10.

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