Lesson eLearning

Find the equation of the line of symmetry of the triangle with vertices ((0,0), (4,0)) and ((2,3)).

hard 3 marks Class 7 · Mathematics · Symmetry
Answer
x=2

The correct answer is x=2 — Checking distances: the distances from ((0,0)) and ((4,0)) to the line (x=2) are equal, confirming symmetry.

Step-by-step solution

  1. The base of the triangle lies along the line (y=0) from (x=0) to (x=4).
  2. For a line to be an axis of symmetry it must map vertex ((2,3)) onto itself, so the line must be vertical and pass through the midpoint of the base.
  3. The midpoint of ((0,0)) and ((4,0)) is ((2,0)).
  4. Thus the vertical line through (x=2) is the line of symmetry.
  5. Checking distances: the distances from ((0,0)) and ((4,0)) to the line (x=2) are equal, confirming symmetry.
Common mistake: assuming the horizontal line (y=1.5) is the axis of symmetry

Concept tested: symmetry of triangles in coordinate geometry

Published · How this solution was prepared and checked

← All Symmetry questions