Math Problem Statement
YAY
Solution
The question in the image asks to determine the coordinates of point that divides the line segment in the ratio . The coordinates of and are given, and intermediate steps show how to compute the slope, the run, and the rise.
Here's a breakdown of the steps involved:
-
Coordinates of points:
- Point is located at .
- Point is located at .
-
Slope of the line: The slope of the line is calculated using the formula: This value is correctly computed in the image.
-
Ratio and division of the segment: The ratio of the division is , meaning that the point divides the segment into two parts where one part is (since ) of the total length.
-
Run and rise:
- The total run (horizontal change) from to is units (from to ).
- Taking of the run: . Thus, the x-coordinate of is .
- The total rise (vertical change) is units.
- Taking of the rise: . So, the y-coordinate of is .
-
Coordinates of point : Thus, point is located at .
Solution Summary:
- Point , which divides in the ratio , is located at .
Would you like more details on any step or a deeper explanation?
Here are five related questions to explore:
- How is the concept of slope useful in determining points along a line?
- What are other methods to divide a line segment into a given ratio?
- Can you apply the midpoint formula to verify the division of the segment?
- How do you generalize this to find a point dividing any two points in a ratio ?
- What would the coordinates be if the ratio was reversed, say ?
Tip: The formula to divide a line segment in the ratio between two points and is:
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Coordinate Geometry
Line Division
Ratios
Formulas
Slope formula: m = (y2 - y1) / (x2 - x1)
Division of line segment in a ratio m:n: (mx2 + nx1) / (m+n), (my2 + ny1) / (m+n)
Theorems
Coordinate Geometry Theorem for Line Segment Division
Suitable Grade Level
Grades 9-11
Related Recommendation
Titik C Membagi Ruas Garis AB Dalam dan Diluar Perbandingan 4:1
Coordinate Geometry: Dividing a Line Segment AB by Point C in Ratios 1:2 and 4:3
Find Point C Dividing Line Segment AB in Ratio 4:1 in 3D Space
Equation of a Line Perpendicular to a Segment Dividing in Ratio 1:3
Find Coordinates of Point G Using Section Formula in Ratio 3:5