Translating to a Line Through the Origin
- I-Heng McComb
Choosing a Translation
Add a translation vector to diagram which will map Point A to the origin. What is the translation vector in component notation?
We can describe the translation as (x,y) --> (x',y'). Give algebraic expressions for x'and y' in terms of x and y.
Image of the Line
Now use your translation vector to translate Line AB. The result should be a line through the origin. We can write an equation y' = ___ x' for Line A'B', where (x',y') represents any point on the image line. What is the equation in this case?
Equation of the Line
What equation do you get when you write your equation for Line A'B' in terms of x and y (the coordinates before you translated)?
Slope-Intercept Form Equation
Rewrite your equation for Line AB in slope-intercept (y = mx + b) form. (Does the equation you found have the correct y-intercept? Move the graphic view to find out!)