Question

1. triangle hfg and points h, f and g are shown on the coordinate grid. which rule best represents the transformation applied to △hfg to create △hfg? a) (x,y)→( - x,y) b) (x,y)→(x - 7,y + 2) c) (x,y)→(x, - y) d) (x,y)→(x + 7,y - 2)

Explanation:

Step1: Analyze translation rules

Translation in a coordinate - plane is of the form $(x,y)\to(x + a,y + b)$ where $a$ is the horizontal displacement and $b$ is the vertical displacement. Reflection over the $y$ - axis is $(x,y)\to(-x,y)$ and reflection over the $x$ - axis is $(x,y)\to(x, - y)$.

Step2: Observe the triangles

By observing the positions of $\triangle HFG$ and $\triangle H'F'G'$ on the grid, we can see that the transformation is a translation. If we consider a point $(x,y)$ of $\triangle HFG$ and its corresponding point $(x - 7,y+2)$ of $\triangle H'F'G'$.

Answer:

b) $(x,y)\to(x - 7,y + 2)$