Math Problem Statement
given point C is (-1, 7) and D is (5,1), find 1/3 of the way from D to C
Solution
To find the point that is of the way from point D to point C, we can use the section formula. The coordinates of point C are and point D are .
Using the formula for dividing a line segment in the ratio :
Here, (the part we want) and (the remaining part), giving us the ratio .
Substituting the coordinates of points C and D:
- ,
- ,
Now, substituting these values into the formula:
Thus, the point that is of the way from D to C is .
Summary:
The point of the way from D to C is .
Would you like further details or have any questions? Here are some related questions to consider:
- What is the distance between points C and D?
- How do you calculate the midpoint between two points?
- Can you explain the section formula in more detail?
- What happens if you want to find a point halfway between C and D?
- How can you apply this concept to three-dimensional points?
Tip: Always double-check the ratios when using the section formula to ensure accuracy.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Coordinate Geometry
Section Formula
Formulas
Section formula: (mx2 + nx1) / (m+n), (my2 + ny1) / (m+n)
Theorems
Section theorem
Suitable Grade Level
Grades 9-12
Related Recommendation
Find 1/3 of the Way Between Points (5, 1) and (-1, 7)
Find a Point Dividing a Line Segment in 3D: Two-Thirds from (3, 4, -1) to (3, -1, -4)
Finding Point C on Line Segment AB Using Ratio Division
Find Coordinates of Point B Given Point C on a Line Segment Problem
Find Coordinates of Point E Using Section Formula - Math Problem Solution