Question

4 multiple choice 1 point the table represents the location of qrst before and after a reflection. what is the location of t’ on the coordinate plane? pre-image image q(-9, -8) q’(9, -8) r(-9, -2) r’(9, -2) s(-4, -2) s’(4, -2) t(-4, -8) ? t’(-4, -8) t’(4, -8) t’(-4, 8) t’(4, 8)

Explanation:

Step1: Identify the reflection rule

Looking at the pre - image and image points for Q, R, and S:

• For \(Q(-9,-8)\) and \(Q'(9,-8)\), the \(x\) - coordinate changes sign (\(-9\to9\)) and the \(y\) - coordinate remains the same (\(-8\to - 8\)).
• For \(R(-9,-2)\) and \(R'(9,-2)\), the \(x\) - coordinate changes sign (\(-9\to9\)) and the \(y\) - coordinate remains the same (\(-2\to - 2\)).
• For \(S(-4,-2)\) and \(S'(4,-2)\), the \(x\) - coordinate changes sign (\(-4\to4\)) and the \(y\) - coordinate remains the same (\(-2\to - 2\)).

So the reflection rule is a reflection over the \(y\) - axis. The rule for reflection over the \(y\) - axis is \((x,y)\to(-x,y)\)? Wait, no, in our case, \((-x,y)\to(x,y)\), which is equivalent to \((x,y)\to(-x,y)\) reversed. Wait, actually, if the pre - image is \((x,y)\) and the image is \((-x,y)\) when reflecting over the \(y\) - axis? Wait, no, let's check the coordinates again. For \(Q(-9,-8)\) (pre - image) and \(Q'(9,-8)\) (image), the \(x\) - coordinate of the pre - image is \(-9\), and the \(x\) - coordinate of the image is \(9=-(-9)\). So the rule is: if the pre - image point is \((x,y)\), the image point after reflection over the \(y\) - axis is \((-x,y)\)? Wait, no, \(x=-9\), \(-x = 9\), so yes, the rule is \((x,y)\to(-x,y)\) for reflection over the \(y\) - axis. Wait, but in our case, the pre - image \(Q\) is \((-9,-8)\) and the image \(Q'\) is \((9,-8)\), so \(-x=9\) when \(x = - 9\), so the rule is \((x,y)\to(-x,y)\) (reflection over \(y\) - axis).

Step2: Apply the rule to point T

The pre - image point \(T\) is \((-4,-8)\). Using the reflection rule over the \(y\) - axis \((x,y)\to(-x,y)\), here \(x=-4\), so \(-x = 4\), and \(y=-8\) remains the same. So the image point \(T'\) has coordinates \((4,-8)\).

Answer:

B. \(T'(4, - 8)\) (assuming the option with \(T'(4,-8)\) is the correct one, as per the analysis. If the options are labeled, for example, if the option with \(T'(4,-8)\) is option B, then the answer is B. \(T'(4, - 8)\))