Math Problem Statement
Point F, which is 2/3 the distance from E to C. The coordinate of E is -3,-1 and C is 0,-4. So what is the coordinates of point F
Solution
To find the coordinates of point , which is of the way from to , we can use the section formula for internal division of a line segment in a given ratio.
The formula for the coordinates of a point dividing a line segment between and in the ratio is:
Here, (since the ratio is , the point divides the line in the ratio 2:1), , and .
Now we can calculate the coordinates of point .
For the x-coordinate:
For the y-coordinate:
So, the coordinates of point are .
Would you like further details or have any questions?
Here are some related questions to explore:
- How do you calculate the midpoint between two points?
- Can you apply the section formula to divide a line externally?
- What happens when the ratio is reversed?
- How would you find the equation of a line passing through points and ?
- How can we verify that lies on the line between and ?
Tip: The section formula can be used for both internal and external division of a line segment.
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Math Problem Analysis
Mathematical Concepts
Coordinate Geometry
Section Formula
Ratios
Formulas
Section formula for internal division: (x, y) = ((mx2 + nx1) / (m + n), (my2 + ny1) / (m + n))
Theorems
Section formula for dividing a line segment in a given ratio
Suitable Grade Level
Grades 9-11
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Find Coordinates of Point E Using Section Formula - Math Problem Solution