Question

δabc is transformed using a sequence of transformations. a) reflection across the y - axis b) rotation 90° clockwise. which triangle shows the final image? 1 2 3 4

Explanation:

Step1: Apply y - axis reflection rule

The rule for reflecting a point $(x,y)$ across the $y$-axis is $(-x,y)$. Let the vertices of $\triangle ABC$ be $(x_1,y_1),(x_2,y_2),(x_3,y_3)$. After reflection across the $y$-axis, the new vertices are $(-x_1,y_1),(-x_2,y_2),(-x_3,y_3)$.

Step2: Apply 90 - degree clockwise rotation rule

The rule for rotating a point $(x,y)$ 90 degrees clockwise about the origin is $(y, - x)$. Apply this rule to the vertices obtained from the reflection step. Let the vertices after reflection be $(a_1,b_1),(a_2,b_2),(a_3,b_3)$. After rotation, the final vertices are $(b_1,-a_1),(b_2,-a_2),(b_3,-a_3)$.
If we consider the general transformation of the triangle's vertices step - by - step as above, we can analyze the orientation and position of the final triangle. A reflection across the $y$-axis flips the triangle to the opposite side of the $y$-axis, and a 90 - degree clockwise rotation then rotates it in the clockwise direction around the origin.
When we perform these two transformations on $\triangle ABC$, we find that the final image is triangle 1.

Answer:

1