Question

triangle ghw is graphed on a coordinate plane. the transformations listed below are performed on triangle ghw.
. r: reflection across the line x = - 4
. t: translation so that (x, y)→(x + 1,y - 2)
select the letter that corresponds to the triangle shown on the coordinate plane below that is the result of performing transformation r, followed by transformation t, on triangle ghw.

Explanation:

Step1: Reflection across x = - 4

Let a point on the original triangle be $(x,y)$. The formula for reflection across the vertical line $x = a$ is $(2a - x,y)$. Here $a=-4$, so the new - x - coordinate after reflection across $x = - 4$ is $2(-4)-x=-8 - x$, and the y - coordinate remains the same. So the transformation of a point $(x,y)$ after reflection across $x=-4$ is $(-8 - x,y)$.

Step2: Apply the translation

The translation rule is $(x,y)\to(x + 1,y - 2)$. After applying the translation to the point $(-8 - x,y)$ from the previous step, we get $(-8 - x+1,y - 2)=(-7 - x,y - 2)$.
We can take a vertex of the original triangle, say $(0,0)$. After reflection across $x=-4$, it becomes $(-8,0)$. After translation, it becomes $(-8 + 1,0 - 2)=(-7,-2)$.
We can repeat this process for other vertices of the original triangle and then match the resulting triangle with the options given on the coordinate - plane.

(Without the specific coordinates of the original triangle vertices and the clear - cut visual matching of the final triangle among the options A, B, C, D in a non - blurry way, we assume we have done the general transformation steps. If we had the original triangle vertices: Let the vertices of the original triangle be $(x_1,y_1),(x_2,y_2),(x_3,y_3)$. After reflection across $x=-4$: $( - 8 - x_1,y_1),( - 8 - x_2,y_2),( - 8 - x_3,y_3)$. After translation: $( - 7 - x_1,y_1 - 2),( - 7 - x_2,y_2 - 2),( - 7 - x_3,y_3 - 2)$)

Since we don't have enough clear information about the original triangle vertices and the exact visual match among the options from the blurry image, we can't give a definite letter answer. But the general process to find the answer is as above.

If we assume we have calculated the new vertices for all options and compared:

Answer:

[We need more clear information about the original triangle vertices and the options on the non - blurry image to give a specific answer like A. Triangle A, B. Triangle B, etc.]