(b) (1) For each point in the diagram below, draw the reflection of the point about the \( x \)-axis and indicate the coordinates of the image. (2) Rewrite and complete the following: \( \mathrm{A}(-3 ; 4) \rightarrow \mathrm{A}^{\prime}( \); ) \( \mathrm{B}(-5 ; 2) \rightarrow \mathrm{B}^{\prime}(~ ; ~) \) \( \mathrm{C}(0 ; 3) \rightarrow \mathrm{C}( \); ) \( \mathrm{D}(6 ;-2) \rightarrow \mathrm{D}( \); ) \( \mathrm{E}(2 ;-5) \rightarrow \mathrm{E}^{\prime}(~ ;) \) (3) What do you notice? (4) Write down, in words, a rule for reflecti) Conclusion

: (1) To draw the reflection of a point about the \( x \)-axis, you need to keep the \( x \)-coordinate the same and change the sign of the \( y \)-coordinate. Here are the reflections and their coordinates: - \( \mathrm{A}(-3 ; 4) \rightarrow \mathrm{A}^{\prime}(-3 ; -4) \) - \( \mathrm{B}(-5 ; 2) \rightarrow \mathrm{B}^{\prime}(-5 ; -2) \) - \( \mathrm{C}(0 ; 3) \rightarrow \mathrm{C}^{\prime}(0 ; -3) \) - \( \mathrm{D}(6 ; -2) \rightarrow \mathrm{D}^{\prime}(6 ; 2) \) - \( \mathrm{E}(2 ; -5) \rightarrow \mathrm{E}^{\prime}(2 ; 5) \) (2) The completed table is as follows: \( \mathrm{A}(-3 ; 4) \rightarrow \mathrm{A}^{\prime}(-3 ; -4) \) \( \mathrm{B}(-5 ; 2) \rightarrow \mathrm{B}^{\prime}(-5 ; -2) \) \( \mathrm{C}(0 ; 3) \rightarrow \mathrm{C}^{\prime}(0 ; -3) \) \( \mathrm{D}(6 ; -2) \rightarrow \mathrm{D}^{\prime}(6 ; 2) \) \( \mathrm{E}(2 ; -5) \rightarrow \mathrm{E}^{\prime}(2 ; 5) \) (3) Upon observing the reflections, you notice that the \( x \)-coordinates remain the same, while the \( y \)-coordinates are negated (i.e., their signs are reversed). (4) The rule for reflecting a point about the \( x \)-axis is: to find the image of a point \( (x, y) \), keep the \( x \)-coordinate the same and change the sign of the \( y \)-coordinate to \( -y \).