Question

the rule t y - axis o r 90°(x, y) is applied to △abc. which triangle shows the final image? 1 2 3 4

Explanation:

Step1: Recall rotation rules

The rule $R_{90^{\circ}}(x,y)=(-y,x)$ means a 90 - degree counter - clockwise rotation about the origin. When we rotate a point $(x,y)$ 90 degrees counter - clockwise about the origin, the $x$ and $y$ coordinates are transformed as above.

Step2: Analyze the orientation of the triangle

For a right - angled triangle, a 90 - degree counter - clockwise rotation will change its orientation. The hypotenuse and the legs of the triangle will be in new positions relative to the axes.

Step3: Match with the given triangles

By visual inspection and applying the rotation rule conceptually to the vertices of $\triangle ABC$, we can see that the final image after the rotation will match one of the given triangles. In a 90 - degree counter - clockwise rotation, the triangle that was originally in the third - quadrant will end up in the second - quadrant with its orientation changed according to the rotation rule. After rotation, triangle 1 shows the correct orientation and position of the rotated $\triangle ABC$.

Answer:

1.