Finding the End Point of a Transformed Vector

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SUMMARY

The discussion centers on calculating the endpoint of a transformed vector in a 2D coordinate system, specifically from the point (10,20) at an angle of 30 degrees clockwise from an initial line to (210,200). The user attempted to apply the distance formula but faced challenges due to missing variables. The correct approach involves using trigonometric functions to determine the x and y components of the second line based on the specified angle and length, ultimately leading to the endpoint calculation.

PREREQUISITES
  • Understanding of 2D coordinate systems
  • Familiarity with trigonometric functions (sine and cosine)
  • Knowledge of vector addition
  • Proficiency in using the distance formula
NEXT STEPS
  • Study vector transformations in 2D space
  • Learn how to apply trigonometric functions to find vector components
  • Explore the distance formula and its applications in coordinate geometry
  • Practice solving problems involving angles and lengths in vector calculations
USEFUL FOR

Students in mathematics or computer graphics, educators teaching vector mathematics, and anyone interested in geometric transformations and their applications in programming.

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Homework Statement


The origin (0,0) is in the upper left corner of the image. +x axis goes to the right while +y axis goes down. The artist draws a line from the pixel location (10,20) to the location (210,200) . She wishes to draw a second line that starts at (10,20), is 270 pixels long, and is at angle of 30deg measured clockwise from the first line. At which pixel location should this second line end? Give your answer to the nearest pixel.
 
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Where are your relevant equations? Where's your attempt at a solution?
 
ideasrule said:
Where are your relevant equations? Where's your attempt at a solution?

I tried solving for the magnitude, but realized I had two missing variables i had to solve for
250=sqrt[(10+x)^2 + (20+y)^2] .. this didn't work
i tried adding the first two vectors to get (220,220) but didn't know what to do after that

i'm just lost...
 

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