A is the only choice that correctly identifies her error. When reflecting over the y-axis, you should always negate the x-value, not the y-value. So, point P’ should be (-3,7) instead of (3,-7). B does not correctly identify a mistake because sometimes, in a reflection, certain points do not move. On point Q, we would have negated 0, but since -0 does not exist, the point will simply stay the same. C does not correctly identify a mistake because because the x-value that was negated (-5), was correctly negated. Choice D also does not correctly identify a mistake because the y-axis is he vertical axis. Finally, choice E does not identify a mistake either because she did not switch the coordinates of P’ when she graphed them. :)
Arionna is trying to reflect the graph across the y-axis, also known as the vertical axis. Therefore, we can immediately eliminate the fourth statement:
"Arionna's red triangle should be reflected below the horizontal axis rather than across the vertical axis."
When comparing the original graph to its reflection, all new points will have the same y-value but negative x-values. Therefore, we can also eliminate the third statement:
"Arionna did not find the correct value for R'. she should have negated the y-value, not the x-value."
With this knowledge in mind, we can see that Point Q' was correctly reflected. The original point was given as (0,4). After reflection, we can see that 0 keeps its value of 0 and 4 keeps its value of 4. Therefore, we can also eliminate the second statement:
"Arionna did not find the correct value for Q'. All points in a reflection will move."
We now see that Arionna made a mistake when reflecting Point P. According to her work, she negated the y-value and kept the x-value. We know that she should have done the opposite. Therefore, we can confirm the first statement:
"Arionna did not find the correct point for P'. she should have negated the x-value, not the y-value."
According to her table, Arionna calculated that Point P (3,7) would reflect to become point (3,-7). This is a mistake (addressed in the previous statement). However, she made another mistake when trying to graph this point. Instead of graphing the new point as the calculated (3,-7), she graphed it as (-7,3). Therefore, we can confirm the fifth statement:
"Arionna switched the order of the coordinates of P' (3,-7) when she graphed them."
