Which two triangles go together as the pre-image and the reflected image?

Question

1 and 2

2 and 3

3 and 4

1 and 4

Answer 1

Two of the triangles are reflected across an axis. To get the answer imagine folding the graph along first the x and then the y axis. When you do that you should see that two triangles fit on atop the other perfectly, and those are the two triangles that are the pre image and the reflected image.

Answer 2

This is really about having a mental image of what a mirror does. When you point towards a mirror, your reflection also points toward the mirror (from the perspective that your image is behind the mirror) on the same side (from your perspective).

For instance, when you bring your hand towards the mirror, your image's hand comes to meet yours on the mirror surface.

So, let's think of the x and y-axes as mirrors. Which triangles look like mirror images of each other?

2 is pointing towards the mirror, but 1 is pointing away from it, so they cannot be mirror images.

Likewise, 1 pointing towards the mirror, but 4 is not

3 is pointing towards the mirror, and 4 is also doing so, but with the wrong "hand". They'll never "meet", so not mirror images.

This leaves 2 and 3. They're both pointing at the mirror with "hands" on the same side. Every point in 2 is equally distant from the mirror as the corresponding point in 3, so 2 and 3 are mirror images.

There's a more precise way to word all of this (in terms of geometry), but when you see "pre-image" and "reflected image", think of seeing yourself (or the thing you are looking at) in the mirror.