Question

triangle hjk is graphed on the coordinate grid. triangle hjk will be transformed using the rule (-x,y) to create triangle hjk. which graph represent triangle hjk?

Explanation:

Step1: Understand the transformation rule

The rule $(-x,y)$ reflects a point across the y - axis. That is, if a point has coordinates $(x,y)$ in the original triangle, its new coordinates in the transformed triangle will be $(-x,y)$.

Step2: Analyze the transformation of each vertex

Let's assume the coordinates of $H=(x_1,y_1)$, $J=(x_2,y_2)$ and $K=(x_3,y_3)$ in $\triangle HJK$. After the transformation, the coordinates of $H'=(-x_1,y_1)$, $J'=(-x_2,y_2)$ and $K'=(-x_3,y_3)$. This means that the x - coordinates of all the vertices change their signs and the y - coordinates remain the same. Geometrically, the triangle is reflected across the y - axis.

Step3: Check the options

When we reflect $\triangle HJK$ across the y - axis, the triangle will be on the left - hand side of the y - axis. Looking at the options, option A shows the triangle $\triangle HJK$ reflected across the y - axis.

Answer:

A.