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# How many capital letters of the English alphabets having both horizontal and vertical lines of symmetry are there?

Last updated date: 25th Jul 2024
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Hint: First we have to define what the terms we need to solve the problem are.
The meaning horizontal line is a straight line that is mapped from left to right and then it is parallel to the X-axis in the plane coordinate system (line at which the earth's surface and the sky appear to meet). as vertical is the opposite of horizontal, anything that makes a $90$-degree angle (right angle) with the horizontal is called vertical.

First of all, there are $26$English alphabets there are A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z and now we are going to check which of these alphabets contains both horizontal and vertical lines of symmetry.
We know that in A there is only vertical symmetry (straight line which meats sky with X-axis in plane coordinates) and no horizontal symmetry
Now for B there is only horizontal symmetry and no vertical symmetry (reason as above)
Further proceeding the same way for all $26$ English alphabets,
Only H, I, O, X are having both vertical and horizontal symmetries.
For O a slope of zero, means that the line is horizontal and vertical symmetry (the y-coordinates never change no matter what x-coordinates is)
The number of capitals of the English alphabets having both vertical and horizontal lines of the symmetry is $4$(H, I, O, X)

Note: Symmetry means balanced and proportionate similarity that is found in two halves of an object and something is symmetrical when it is same on both sides.
The meaning horizontal line is a straight line that is mapped from left to right and then it is parallel to the X-axis in the plane coordinate system (line at which the earth's surface and the sky appear to meet).