31. The number of capital letters of the English alphabet having only a vertical line of symmetry is ____.
Answer: 7 (A, M, T, U, V, W, Y)
Beginner-friendly Explanation (step by step)
- What is a vertical line of symmetry?
If you can draw a vertical (up–down) line through the middle of a shape or letter, and the left side is a mirror image of the right side, then the letter has vertical symmetry.
- What does “only vertical” mean?
The letter must have vertical symmetry, but it must not have horizontal symmetry (i.e., it should not look the same when split by a left–right line through the middle).
- Letters that have both vertical and horizontal symmetry (so we must EXCLUDE them):
H, I, O, X
These look the same with a vertical line and also with a horizontal line through the middle, so they are not “only vertical”.
- Now check each candidate letter one by one:
- A: Vertically symmetric (left and right slants match). Not horizontally symmetric (top triangle ≠ bottom). Keep
- M: Vertically symmetric (two sides reflect across the middle). Not horizontally symmetric (top peaks ≠ bottom ends). Keep
- T: Vertically symmetric (equal left–right). Not horizontally symmetric (top bar ≠ bottom stem). Keep
- U: Vertically symmetric (curves match). Not horizontally symmetric (open at top ≠ bottom). Keep
- V: Vertically symmetric (two equal slants). Not horizontally symmetric (point at bottom ≠ open at top). Keep
- W: Vertically symmetric (mirror across center). Not horizontally symmetric (points and openings don’t match top vs bottom). Keep
- Y: Vertically symmetric (arms match across center). Not horizontally symmetric (forked top ≠ single stem bottom). Keep
- Count them: A, M, T, U, V, W, Y → 7 letters.
Note: We consider the usual block/print style for capital letters. Some fonts may vary slightly, but the standard school font follows the rules above.