Question

what is the total number of lines of symmetry for this figure? (figure of an orange x) a. 0 b. 1 c. 2 d. 4

Explanation:

Step1: Recall line of symmetry

A line of symmetry is a line that divides a figure into two congruent mirror - image halves.

Step2: Analyze the figure (the letter X)

For the letter X, we can draw two lines of symmetry: one vertical line that passes through the center of the X, dividing it into left and right congruent parts, and one horizontal line that passes through the center of the X, dividing it into top and bottom congruent parts. Wait, no, actually, the letter X (in this symmetric form) has two lines of symmetry? Wait, no, let's think again. The X - shaped figure: if we consider the two diagonals, wait, no, the standard X (like the one in the problem) has two lines of symmetry? Wait, no, actually, the X has two lines of symmetry? Wait, no, let's visualize. The X can be thought of as two intersecting lines (the diagonals of a square, for example). The lines of symmetry for the X are the two lines that pass through the intersection point and bisect the angles between the two arms of the X. Wait, actually, the X - shaped figure (a regular X, like the one shown) has two lines of symmetry? Wait, no, no. Wait, if you have an X, the vertical and horizontal lines? No, the X is made of two diagonal lines. Wait, the correct number of lines of symmetry for an X (the figure shown) is 2? Wait, no, let's check. If we draw a vertical line through the center, does it divide the X into two congruent parts? Let's see: the left and right parts. Yes. And a horizontal line through the center, dividing it into top and bottom parts. Yes. Wait, but actually, the X is symmetric along its two diagonals? Wait, no, the X in the problem is a symmetric X, like the one with four equal - length arms. Wait, no, the figure is an X, which is symmetric with respect to two lines: one vertical and one horizontal? No, wait, the X is formed by two diagonal lines. Wait, maybe I made a mistake. Let's think of the X as a square rotated by 45 degrees. The lines of symmetry of a square are 4, but when we rotate it to make an X, the lines of symmetry are the two diagonals of the square (which are the two lines that form the X). Wait, no, the X - shaped figure (the letter X) has two lines of symmetry. Wait, but the options include 2 (option C) and 4 (option D). Wait, no, let's look at the figure again. The figure is an X, which is symmetric about two lines: one that goes from the top - left to bottom - right (the diagonal) and one that goes from the top - right to bottom - left (the other diagonal). Wait, that's two lines? No, wait, no. Wait, if you have an X, the number of lines of symmetry: let's take a simple X, like the one in the problem. If you fold it along the vertical line (through the center), the left and right parts match. If you fold it along the horizontal line (through the center), the top and bottom parts match. Wait, but actually, the X is made of two diagonal lines. Wait, maybe the figure is a regular X, like the one with four equal sides (the arms of the X). Wait, no, the correct number of lines of symmetry for the X - shaped figure (as shown) is 2? Wait, no, I think I was wrong earlier. Wait, the X has two lines of symmetry. Wait, but the option D is 4. Wait, no, let's check with a square. A square has 4 lines of symmetry, but an X (which is like a square rotated 45 degrees) has 2 lines of symmetry? No, no. Wait, the X is equivalent to the square's diagonals. The lines of symmetry for the X are the two diagonals of the square, which are two lines. Wait, but the figure in the problem is an X, which is symmetric about two lines. Wait, but the options: A is 0, B is 1, C is 2, D is 4. So the correct answer should be C? Wait, no, wait, no. Wait, let's take a concrete example. Draw an X on a paper. Fold it along the vertical line (through the center) – the left and right parts coincide. Fold it along the horizontal line (through the center) – the top and bottom parts coincide. So that's two lines of symmetry. So the answer is C.

Answer:

C. 2