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 across x = - 1

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

Step2: Translation

After reflection, we apply the translation $(x,y)\to(x + 4,y + 3)$. So the final transformation for a point $(x,y)$ is $x''=-x - 2+4=-x + 2$ and $y''=y + 3$.
We can take a vertex of triangle GHJ, say G. Let's assume the coordinates of G are $(x_G,y_G)$. After reflection across $x=-1$, its x - coordinate becomes $-x_G - 2$ and y - coordinate remains $y_G$. Then after translation, its x - coordinate is $-x_G - 2+4=-x_G+2$ and y - coordinate is $y_G + 3$.
By applying these transformations to all vertices of triangle GHJ and comparing with the given triangles A, B, C, D on the coordinate - plane, we find the resulting triangle.

Answer:

B. triangle B