the vertices of triangle ABC are A(-1,1), B(0,3) and C(3,4). need help - don't understand problem.

Question

the vertices of tr. ABC are A(-1,1), B(0,3) and C(3,4).  Graph the image of triangle ABC after a composition of the following transformations in the order they are listed.

 

Rotation: 90 degrees counterclockwise about the origin

 

 

reflection: in the y-axis

 

yes/no  if the transformation were performed in reverse order (reflection, then rotation), would the final image be the same?

yes/no  Would the reflection of triangle ABC in the line y=x have produced the same final image?

Answer 1

Hi Kathryn,

 

THX for admitting that you don’t understand the problem.  I’ll try to help you understand it rather than solve it for you.

The three points A, B, and C have (x,y) coordinates that you can plot on the x-y plane.  They form a triangle.  The three points are the vertices of the triangle.

Graph the image. This is an important step.  I’d recommend graphing the original image, then perform the transformations to get a final image, then re-do the transformations in reverse order (as required), then answer the questions.

Now, the transformations:  “Rotate the image 90 degrees counterclockwise about the origin.”  A positive angle (+90) of rotation usually means counter-clockwise and 90 degrees would take the x-axis to the y-axis, so each side of the new triangle is perpendicular to its original position.  Of course, the origin is the point (0,0).

“Reflect in the y-axis” acts like a mirror (the y-axis is the edge of the mirror).  So, for example, point (5,3) will become (5,-3).

Actually, you, or a computer, could perform these transformations without a picture, but pictures really help us humans.  In fact, programs like MS Word, MS PowerPoint, etc. have this capability built-in –- just insert a shape, then select it and (Format then) rotate or flip it.

Now, a reflection in the line y=x is a little trickier.  The line y=x goes from the origin (0,0) to the upper right at an angle of 45 degrees.  So, drawing this part of your solution is a lot easier than calculating an answer.  Imagine folding your graph on that y=x line then seeing the triangle in its new position as though you had transparent paper. 

The purpose of this problem is to determine whether the order of operations makes a difference.  You can perform these tasks now to see.  I hope you understand it now !

 

Here’s another example, Don lives 5 blocks down and 2 blocks left.  Is that the same as 2 blocks left and 5 blocks down?  Is that the same as 5 blocks left and 2 blocks down?