Question

translate triangle abc, with vertices at (2, -4) (-4, 4) (-1, 3), 6 units to the right and 1 unit up. which image illustrates the result? a image of a triangle b image of a triangle c image of a triangle d image of a triangle

Explanation:

Step1: Define translation rule

For a point $(x,y)$, translating 6 right and 1 up gives $(x+6, y+1)$.

Step2: Calculate new vertices

• For $(2, -4)$: $2+6=8$, $-4+1=-3$ → $(8, -3)$
• For $(-4, -4)$: $-4+6=2$, $-4+1=-3$ → $(2, -3)$
• For $(-1, 3)$: $-1+6=5$, $3+1=4$ → $(5, 4)$

Step3: Match to graph

The new vertices $(8, -3)$, $(2, -3)$, $(5, 4)$ form a triangle in the first quadrant/lower right area, which matches image a.

Answer:

The correct image is option a