Question

when the triangle below is translated 1 unit to the left and 2 units down, which of the following is not a vertex of the translated image?
(-3,1)
none of the other answers are correct
(1,2)
(-5,-1)
(-2,-2)

Explanation:

Step1: Recall translation rule

For a translation 1 unit left and 2 units down, the rule for a point $(x,y)$ is $(x - 1,y - 2)$.

Step2: Assume original vertices

Let's assume we find the original vertices of the triangle from the graph (not shown here in full - but conceptually). If we had an original vertex $(x,y)$, the new vertex after translation would be $(x-1,y - 2)$.

Step3: Check each option

For option A: If we assume the original point was $(-2,3)$ then $(-2-1,3 - 2)=(-3,1)$.
For option C: If the original point was $(2,4)$ then $(2-1,4 - 2)=(1,2)$.
For option D: If the original point was $(-4,1)$ then $(-4-1,1 - 2)=(-5,-1)$.
For option E: If the original point was $(-1,0)$ then $(-1-1,0 - 2)=(-2,-2)$.

Answer:

None of the other answers are correct