Math Problem Statement
Calculate the exact distance between the points (-2, 3) and (4, 9).
A.)
12 B.)
2 square root of 10 C.)
5 square root of 2 D.)
6 square root of 2
Solution
To calculate the exact distance between the points and , we use the distance formula:
Plugging in the coordinates and :
Calculate the differences:
Substitute these into the distance formula:
So, the exact distance between the points is .
Therefore, the correct answer is:
D.)
Would you like more details or have any questions? Here are some additional questions to expand your understanding:
- What is the distance formula used to calculate the distance between two points in a plane?
- How do you derive the distance formula from the Pythagorean theorem?
- Can the distance formula be applied in three-dimensional space? If so, how?
- What are the coordinates of the midpoint between and ?
- How would you calculate the slope of the line segment connecting and ?
- What is the equation of the line passing through the points and ?
- How do you determine if two points are collinear with a third point?
- How does the distance formula change if the points are represented in polar coordinates?
Tip: Always simplify your answers to their most reduced form for clarity and precision.
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Math Problem Analysis
Mathematical Concepts
Coordinate Geometry
Distance Formula
Square Roots
Formulas
Distance formula
Theorems
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Suitable Grade Level
Grades 9-12