The line represented by 2y = x + 8 is dilated by a scale factor of k centered at the origin, such that the image of the line has an equation of y-1/2x=2. What is the scale factor?

Question

danthu · Answer

The  scale factor  of the given dilation transformation is calculated as; 1/2    How to use the scale of dilation?  We know that from transformation that  a dilation is a  non - rigid transformation  that produces similar figures.    If two lines are similar, then the lines are  parallel  and parallel lines always have the  same slope.     Thus;  Line A has the formula; 2y = x + 8  Writing it in slope intercept form gives us;  y = 0.5x + 4   ------(1)  Thus;    slope  of the line A is m = 0.5   y-intercept  of the line A is b = 4    Line B has the equation;  y - ¹/₂x = 2  Rearranging in  Slope Intercept form  gives us;  y = ¹/₂x + 2  Thus;    slope  of the line B is m = 0.5   y-intercept  of the line B is b = 2    Now, it should be noted that the y-intercept of line A multiplied by the  scale factor  k must be equal to the y-intercept of line B. Thus;  4k = 2  k = 2/4  k =  ¹/₂    Read more about  Scale of Dilation  at; https://brainly.com/question/10253650    #SPJ1

How to use the scale of dilation?

Leave a Comment Cancel reply