Question

triangle ghu is graphed on a coordinate plane. the transformations listed below are performed on triangle ghu.

• 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 ghu.
a. triangle a
b. triangle b
c. triangle c
d. triangle d

Explanation:

Step1: Apply reflection rule

For a point $(x,y)$ reflected across the line $x = a$, the new - x - coordinate is $2a - x$ and the y - coordinate remains the same. Here $a=-4$, so if a point on $\triangle{GHU}$ has coordinates $(x,y)$, after reflection across $x = - 4$, its new coordinates are $(2\times(-4)-x,y)=(-8 - x,y)$.

Step2: Apply translation rule

After reflection, we apply the translation $(x,y)\to(x + 1,y - 2)$. So the final coordinates of the point are $(-8 - x+1,y - 2)=(-7 - x,y - 2)$.
We can also analyze the effect on key - points of the triangle. For example, if we consider a vertex of $\triangle{GHU}$ and perform the two transformations step - by - step. By comparing the position of the vertices of the original triangle $\triangle{GHU}$ with the transformed triangle after reflection across $x=-4$ and then translation $(x,y)\to(x + 1,y - 2)$, we find that the resulting triangle is the one that matches the characteristics of triangle $D$.

Answer:

D. triangle D