To find the shortest distance Steven must drive to get to his mom’s birthday party, we can calculate the straight-line distance between the two points $(-4, -8)$ and $(6, 3)$ using the distance formula. The distance formula between two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

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

For Steven's journey:

• Starting point $(x_1, y_1) = (-4, -8)$
• Destination $(x_2, y_2) = (6, 3)$

Substitute these values into the distance formula:

$d = \sqrt{(6 - (-4))^2 + (3 - (-8))^2}$ $d = \sqrt{(6 + 4)^2 + (3 + 8)^2}$ $d = \sqrt{(10)^2 + (11)^2}$ $d = \sqrt{100 + 121}$ $d = \sqrt{221}$ $d \approx 14.87 \text{ units}$

Therefore, the closest distance Steven must drive to get to the party is approximately 14.87 units.

Would you like more details on any of the steps or have any other questions?

Here are five related questions you could explore:

1. How would the calculation change if Steven took a detour along the x-axis and y-axis?
2. How can we find the slope of the line connecting these two points?
3. What is the midpoint of the line segment connecting Steven's house and the party location?
4. How would the distance formula change in three dimensions?
5. How can you use the Pythagorean theorem to confirm this result?

Tip: When applying the distance formula, always check that you've correctly squared the differences in both coordinates to avoid common mistakes.