Math Problem Statement

What is the closest distance in units Steven must drive to get to the party?

Solution

To find the closest distance Steven must drive to get from his house to the party, we can use the distance formula between two points in a coordinate plane.

The coordinates of Steven's house are (4,8)(-4, -8) and the coordinates of the party are (6,3)(6, 3).

The distance formula is:

d=(x2x1)2+(y2y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

Substituting the coordinates into the formula:

d=(6(4))2+(3(8))2d = \sqrt{(6 - (-4))^2 + (3 - (-8))^2} d=(6+4)2+(3+8)2d = \sqrt{(6 + 4)^2 + (3 + 8)^2} d=102+112d = \sqrt{10^2 + 11^2} d=100+121d = \sqrt{100 + 121} d=221d = \sqrt{221} d14.87d \approx 14.87

So, Steven must drive approximately 14.87 units to get to the party.

Would you like further details on how the distance formula works, or do you have any questions?

Here are some related questions you can explore:

  1. What is the formula for calculating the distance between two points in 3D space?
  2. How can the Pythagorean theorem be used to derive the distance formula?
  3. What are some real-life applications of the distance formula in navigation?
  4. How would the distance change if Steven's house or the party's location were shifted by one unit?
  5. How is the midpoint of a line segment calculated between two points?

Tip: Always double-check the signs of the coordinates when using the distance formula to avoid calculation errors!

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Distance Formula

Formulas

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 7-9