Question

below is shown a triangle in a grid. which of the following transformations changes the original orientation of the triangle by 90 degrees?

Explanation:

To determine which transformation rotates the triangle by 90 degrees, we analyze each option:

1. The first option (top - most choice) appears to be a rotation (likely 90 - degree) as the triangle’s orientation is turned 90 degrees relative to the original (original has the base horizontal, this has a side vertical/horizontal in a rotated way).
2. The second option is a reflection (upside - down, 180 - degree - like flip, not 90 - degree rotation).
3. The third option: Let's check the orientation. The original triangle has a vertical axis of symmetry (base horizontal, apex up). The third option's triangle has a horizontal axis of symmetry (apex right, base vertical), which is a 90 - degree rotation (either clockwise or counter - clockwise). Wait, actually, let's re - evaluate. Wait, the original triangle: base is horizontal, apex is up. A 90 - degree rotation (say, clockwise) would make the base vertical and apex to the right. Let's check the third option: the triangle has its base vertical (along the y - axis) and apex to the right (along the x - axis). Yes, that's a 90 - degree rotation. Wait, maybe I mis - identified the first option. Wait, the first option: the triangle seems to be a rotation but maybe not 90. Wait, let's look at the third option (the one with the triangle pointing to the right, base vertical). The original triangle: base horizontal (length, say, 3 units), height vertical (say, 3 units). A 90 - degree clockwise rotation would make the base vertical (length 3) and height horizontal (length 3), with the apex pointing to the right. That matches the third option. The fourth option is a translation (moved, same orientation). The second is a reflection (flipped vertically, 180 - degree orientation change? No, reflection over x - axis would flip it, but orientation change is 180? Wait, no. A reflection changes orientation but not by 90. A rotation by 90 degrees changes the orientation such that the angles between the sides and the axes change by 90. So the third option (the triangle pointing to the right, with base on the y - axis) is a 90 - degree rotation. Wait, maybe the first option was mis - seen. Wait, the original triangle: apex up, base down (horizontal). Let's check each:

• First option: triangle is rotated but maybe 45? No, the third option: apex to the right, base vertical. That's 90 degrees (from apex up to apex right: 90 - degree rotation clockwise).

So the correct option is the third one (the triangle with apex pointing to the right, base along the vertical line through the origin).

Answer:

The third option (the triangle with its apex pointing to the right, base vertical, centered at the origin - like grid point)