Whercise 6,5 find the imags of tirs point \( (0,1) \) when reflected about the line \( y=\sqrt{3} x \). find the imags of the point \( (2,3) \) when reflected about the line \( y=-\sqrt{3} x \). Find the imagg of the point \( (3,0) \) when reflected about the line \( y=2 x \).

To find the image of the point \( (0,1) \) when reflected about the line \( y=\sqrt{3} x \), you can use the formula to reflect a point \( (x_1, y_1) \) about the line \( Ax + By + C = 0 \). For this line, \( A = -\sqrt{3}, B = 1, C = 0 \). The reflection formula gives us the reflected point! After applying the calculations, you'll find that the image of point \( (0,1) \) is \( (2, 0) \). Now, reflecting the point \( (2,3) \) about the line \( y=-\sqrt{3}x \) follows the same method. This time, you'll set \( A = \sqrt{3}, B = 1, C = 0 \). After performing the necessary calculations, the image of point \( (2,3) \) turns out to be \( (1, 5) \). Finally, reflecting the point \( (3,0) \) about the line \( y=2x \) is accomplished using the same reflection technique. For this line, we have \( A = -2, B = 1, C = 0 \). Following through with the calculations, the image of the point \( (3,0) \) results in \( (1, 6) \). In summary, the images of the points are: - \( (0,1) \) reflected about \( y=\sqrt{3}x \) is \( (2, 0) \) - \( (2,3) \) reflected about \( y=-\sqrt{3}x \) is \( (1, 5) \) - \( (3,0) \) reflected about \( y=2x \) is \( (1, 6) \)