Math Problem Statement
Find the midpoint and distance between (7,-3) and (5,2)
Solution
To find the midpoint and distance between the points and , we use the following formulas:
Midpoint Formula:
The midpoint between two points and is given by:
Substitute the coordinates and :
Distance Formula:
The distance between two points and is given by:
Substitute the coordinates and :
Thus, the distance is or approximately .
Final Answer:
- Midpoint:
- Distance:
Would you like more details or have any questions?
Related Questions:
- What is the formula for finding the slope between two points?
- Can you find the equation of the line passing through the points and ?
- How do you find the distance between a point and a line?
- What is the general equation for the circle passing through two points?
- How can you find the centroid of a triangle with given vertices?
Tip: The distance formula is derived from the Pythagorean theorem, which connects the horizontal and vertical distances between two points.
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Math Problem Analysis
Mathematical Concepts
Midpoint
Distance between two points
Coordinate Geometry
Formulas
Midpoint Formula: M = ((x1 + x2)/2, (y1 + y2)/2)
Distance Formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Theorems
Pythagorean Theorem
Suitable Grade Level
Grades 7-9
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