Question

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

• r: reflection across the line x = -1
• t: translation so that (x, y)→(x + 4, y + 3)

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 ghj.
a. triangle a
b. triangle b
c. triangle c
d. triangle d

Explanation:

Step1: Reflection rule

The rule for reflecting a point $(x,y)$ across the line $x = a$ is $(2a - x,y)$. For reflection across $x=-1$, the rule is $(- 2 - x,y)$.

Step2: Translation rule

After reflection, we apply the translation $(x,y)\to(x + 4,y + 3)$. So the combined transformation for a point $(x,y)$ is $((-2 - x)+4,y + 3)=(2 - x,y + 3)$.

Step3: Analyze by vertex - example

Let's assume a vertex of $\triangle GHJ$ has coordinates $(x_0,y_0)$. After the combined transformation, its new coordinates are $(2 - x_0,y_0 + 3)$. We can apply this to all vertices of $\triangle GHJ$. Visually, reflection across $x=-1$ will flip the triangle to the right - hand side of the line $x = - 1$, and then the translation $(x,y)\to(x + 4,y+3)$ will move it 4 units to the right and 3 units up.

Answer:

B. triangle B