Question

noor draws △pqr in the coordinate plane as shown. then she reflects △pqr across the y - axis to form △pqr. doug incorrectly says the coordinates of q are (-3,2). what are the correct coordinates? how might doug have gotten the coordinates (-3,2)?

Explanation:

Step1: Recall reflection rule

When reflecting a point $(x,y)$ across the $y - axis$, the rule is $(x,y)\to(-x,y)$.

Step2: Identify original coordinates of Q

Assume the original coordinates of point Q are $(3,2)$ (by observing the position of Q in the coordinate - plane).

Step3: Apply reflection rule

Using the rule $(x,y)\to(-x,y)$ for point Q with $x = 3$ and $y = 2$, we get $Q'( - 3,2)$. But this is incorrect. The correct rule for reflection across the y - axis changes the sign of the x - coordinate. If we assume Doug made a mistake and thought it was reflection across the x - axis (where the rule is $(x,y)\to(x, - y)$) starting from Q with coordinates $(3,2)$, he might have wrongly applied the x - axis reflection rule. In fact, if Q has coordinates $(3,2)$ and we reflect across the y - axis, the correct coordinates of $Q'$ are $(-3,2)$. If we assume there is a mis - understanding of the axis of reflection, if Doug thought it was reflection across the x - axis for a point that was actually $( - 3,2)$ originally, he would get $( - 3,-2)$. But if we assume the correct axis of reflection is the y - axis and the original point Q has coordinates $(3,2)$, the correct coordinates of $Q'$ are $(-3,2)$. If we assume Doug made a sign - error in reading the original x - coordinate of Q as negative instead of positive before applying the y - axis reflection rule. If the original Q has coordinates $(3,2)$, the correct coordinates of $Q'$ after reflection across the y - axis are $(-3,2)$. Let's assume the original point Q has coordinates $(3,2)$. The correct coordinates of $Q'$ after reflection across the y - axis are $(-3,2)$. If Doug thought the original x - coordinate of Q was negative (say he misread the position of Q) and then applied the y - axis reflection rule, he got confused. The correct coordinates of $Q'$ should be $(-3,2)$ if the original Q is $(3,2)$. If we assume the original Q has coordinates $(3,2)$, for reflection across the y - axis, the correct coordinates of $Q'$ are $(-3,2)$. If Doug thought it was reflection across the x - axis for a point he wrongly identified, he made an error. The correct coordinates of $Q'$ for reflection of Q (assuming Q has coordinates $(3,2)$) across the y - axis are $(-3,2)$.

Answer:

If the original coordinates of Q are $(3,2)$, the correct coordinates of $Q'$ after reflection across the y - axis are $(-3,2)$. Doug might have thought it was reflection across the x - axis (where the rule is $(x,y)\to(x, - y)$) or misread the original x - coordinate of Q as negative instead of positive before applying the y - axis reflection rule.