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: Apply reflection rule

For a point $(x,y)$ reflected across the line $x = - 1$, the new $x$-coordinate is $x'=-1-(x + 1)=-x - 2$, and the $y$-coordinate remains the same, i.e., $y'=y$.

Step2: Apply translation rule

After reflection, we apply the translation $(x,y)\to(x + 4,y + 3)$. So the final coordinates of a point after both transformations are $((-x - 2)+4,y + 3)=(-x + 2,y + 3)$.
We can also analyze the effect on the shape's position. The reflection across $x=-1$ will flip the triangle over this vertical line. Then the translation $(x,y)\to(x + 4,y + 3)$ will move the reflected - triangle 4 units to the right and 3 units up.
By visually inspecting the original triangle and applying these transformation rules step - by - step on the key vertices of the triangle (e.g., the corners), we can determine the final position of the triangle.

Answer:

B. triangle B