Question

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Explanation:

Step1: Recall point symmetry definition

A figure has point symmetry if rotating it \(180^\circ\) around a central point maps it onto itself.

Step2: Analyze each figure

• Figure F: Rotating \(180^\circ\) changes its shape (e.g., the horizontal and vertical segments don't align), so no point symmetry.
• L - shaped arrow: Rotating \(180^\circ\) flips the direction of the arrows, and the shape doesn't match, so no.
• Two triangles (diamond - like): Rotating \(180^\circ\) around the center swaps the triangles, and the figure maps to itself.
• Letter S: Rotating \(180^\circ\) around its center maps the S onto itself (the curves align).
• Triangle (single): Rotating \(180^\circ\) flips it, and the shape doesn't match, so no.

Answer:

The figures with point symmetry are the two - triangle (diamond - like) figure, the letter S figure. (In terms of the checkboxes, the ones corresponding to the two - triangle figure, the S figure, and the L - shaped arrow? Wait, re - checking: Wait, the L - shaped arrow: if we rotate \(180^\circ\), the horizontal arrow becomes vertical and vice - versa? Wait no, let's re - examine. Wait the two triangles: when rotated \(180^\circ\), each triangle's position swaps and the figure looks the same. The S: rotating \(180^\circ\) makes it look like S. The L - shaped arrow: let's see, the first L - shaped (the one with two arrows) – wait, maybe I misidentified. Wait the correct ones are the two - triangle figure, the S figure, and the L - shaped arrow? No, wait the standard point - symmetric figures: S, the two triangles (like a rhombus - made - of - triangles), and the L - shaped with two arrows? Wait no, let's use the definition strictly.

Wait, let's list each figure by their position:

1. Top: F – no.
2. Next: L - shaped (with a horizontal and vertical arrow) – rotating \(180^\circ\): the horizontal arrow becomes vertical downward, vertical arrow becomes horizontal left? No, maybe not. Wait the third figure (two triangles) – yes, rotating \(180^\circ\) swaps them and the figure is same. The fourth figure (S) – yes, \(180^\circ\) rotation maps S to S. The fifth figure (single triangle) – no. Wait also, the L - shaped with two arrows: wait, maybe the second figure (the L - shaped with the two arrows) – when rotated \(180^\circ\), the direction of the arrows flips, but does the shape match? Let's see, the original has a horizontal left arrow and vertical up arrow. Rotating \(180^\circ\) would give horizontal right arrow and vertical down arrow, which is a different shape (the L is flipped). Wait no, maybe I was wrong. So correct ones: the two - triangle figure, the S figure, and maybe the L - shaped? No, let's check standard point - symmetric shapes. S is point - symmetric, the two triangles (forming a parallelogram - like with two triangles) are point - symmetric, and the L - shaped with two arrows? Wait, maybe the answer is the two - triangle figure, the S figure, and the L - shaped arrow? No, let's re - check the image.

Wait the figures are:

1. F – no.
2. A line - shaped (L - like with two arrows) – let's call it Figure 2.
3. Two triangles (Figure 3) – yes.
4. S (Figure 4) – yes.
5. Single triangle (Figure 5) – no.

Wait, maybe Figure 2 (the L - shaped with two arrows) – when rotated \(180^\circ\), the horizontal arrow (left) becomes right, and the vertical arrow (up) becomes down, forming the same L - shape? Wait, no, the original is a left - pointing horizontal arrow and up - pointing vertical arrow (forming an L). Rotating \(180^\circ\) would give a right - pointing horizontal arrow and down - pointing vertical arrow, which is the same L - shape (just flipped). Wait, maybe that's point - symmetric. So:

Figure 3 (two triangles): yes.

Figure 4 (S): yes.

Figure 2 (L - shaped arrows): yes? Wait, no, the L - shape with two arrows: if you rotate \(180^\circ\), the direction of the arrows changes, but the overall L - shape (the angle) is the same? Wait, maybe. So the correct figures are Figure 2 (L - shaped arrows), Figure 3 (two triangles), Figure 4 (S).

But based on standard examples, S is point - symmetric, the two triangles (forming a parallelogram) are point - symmetric, and the L - shaped with two arrows (if it's a rectangle - like L) – maybe. So the checkboxes to select are the ones for the L - shaped arrows, the two - triangle figure, and the S figure.