Question Video: Reflecting a Point Where the Line of Reflection Is Not Horzontal or Vertical Mathematics • First Year of Preparatory School

Video Transcript

Five points are plotted on the grid in the figure below. When reflecting point 𝑃 across the dotted line, which of the four other points will it map onto? Is it option (A) point 𝑄, option (B) point 𝑆, (C) point 𝑇, or (D) point 𝑅?

Remember, a reflection is a transformation that preserves the perpendicular distances of all points from the mirror line. In particular, if we define the image of 𝑃 to be the point 𝑃 prime, this is the reflection through the mirror line where the mirror line is the perpendicular bisector of the line segment that joins these points.

So, we can find the image of 𝑃 by drawing a line perpendicular to the mirror line. That’s the dotted line in this picture. When we do, we see that this perpendicular line passes through point 𝑅. In particular, point 𝑅 is the same perpendicular distance from the dotted line as point 𝑃. So, the correct answer is option (D). Point 𝑅 is the image of 𝑃 in a reflection through the dotted line.