The pre-image of a reflection lies in quadrant II and the image is in quadrant III. which line could be the line of reflection?
a) y=x
b) y=-x
c) x-axis
d) y-axis
if you can then please do explain whay. i have no clue!!! thanks for your help!
draw a circle in quadrant 2
reflect that into quadrant 3
which axis did you reflect around?
If it were around the negative 45 deg line(y= -x), it would never have left quadrant 2
If it were around the positive 45 degree line (y=x) it would have jumped int quadrant 4
If it were around the y axis, it would have moved right into quadrant 1
So, it went the x axis route, down into quadrant 3
thank you so much!!!!!
12 years too late but the answer is y-axis 😏
The orientation of the vertices changed
The reflection can be represented by (-x,y)
To determine the line of reflection for this scenario, let's understand the concept of reflections.
A reflection is a transformation that "flips" an object over a line, called the line of reflection. The line of reflection acts as a mirror, with the object and its reflection being equidistant from the line.
Now, in this particular case, we know that the pre-image (the original shape) lies in quadrant II, and the image (the reflected shape) lies in quadrant III. Quadrant II and quadrant III are opposite sides of the x-axis.
Let's analyze the options one by one:
a) The line y=x is a diagonal line that passes through quadrants I and III. It does not align with the given positions of the pre-image and the image. So, it is not the line of reflection.
b) The line y=-x is a diagonal line that passes through quadrants II and IV. Since the pre-image lies in quadrant II and the image is in quadrant III, this line aligns with the given positions. Therefore, it can be the line of reflection.
c) The x-axis is a horizontal line that does not pass through quadrant II or quadrant III. So, it cannot be the line of reflection in this case.
d) The y-axis is a vertical line that also does not pass through quadrant II or quadrant III. Therefore, it is also not the line of reflection.
Based on this analysis, the line that could be the line of reflection in this scenario is b) y=-x.
Remember, to determine the line of reflection, we need to consider the positions of the pre-image and the image in relation to the axes and identify a line that aligns with their positions.