Which of the following represents the image of point 𝐴 one, three after a reflection about the origin? (A) 𝐴 prime one, negative three. (B) 𝐴 prime negative one, three. (C) 𝐴 prime negative three, negative one. (D) 𝐴 prime negative three, one. Or (E) 𝐴 prime negative one, negative three.
We’re asked to determine the coordinates of the image of a given point following a reflection about the origin. When a point is reflected about the origin, its image appears the same distance away from the origin but on the opposite side. The origin is the bisector of the straight line segment connecting the point and its image.
We can recall the general result that a reflection about the origin maps the general point 𝑃 with coordinates 𝑥, 𝑦 to the point 𝑃 prime with coordinates negative 𝑥, negative 𝑦. In other words, a reflection about the origin maps a point onto its image by changing the signs of both its coordinates.
We can therefore apply this mapping to the point 𝐴, which has coordinates one, three. Changing the sign of both coordinates gives the point 𝐴 prime with coordinates negative one, negative three. Looking carefully at the five options, this is option (E). The image of point 𝐴 one, three after a reflection about the origin is 𝐴 prime negative one, negative three.