Question

1. triangle hjk is graphed on the coordinate grid. triangle hjk will be transformed using the rule ((x,y) \to (x - 8, y)) to create triangle (hjk).

graph of triangle hjk on a coordinate plane

which graph represents triangle (hjk)?

four multiple - choice graph options follow, each showing a triangle on a coordinate plane

Explanation:

Step1: Understand the Transformation

The transformation rule is \((x,y)\to(x - 5,y)\), which means we subtract 5 from the \(x\)-coordinate of each vertex of triangle \(HJK\) to get the vertices of \(H'J'K'\).

Step2: Analyze Each Graph

• For the first graph (top - left): Check the \(x\)-coordinates of the vertices. If the original triangle \(HJK\) has vertices with positive \(x\)-coordinates, subtracting 5 should move them left. This graph shows a leftward shift, which is consistent with the transformation.
• For the top - right graph: The vertices seem to be shifted right or not in the correct direction (subtracting 5 from \(x\) should move left, not right or other directions).
• For the bottom - left graph: The overall position and the direction of the shift (downward component which is not part of the transformation \((x,y)\to(x - 5,y)\) as \(y\)-coordinate remains the same) is incorrect.
• For the bottom - right graph: The vertices seem to be shifted in a way that is not consistent with subtracting 5 from the \(x\)-coordinate (more of a vertical or other non - horizontal left shift).

Answer:

The graph on the Top - Left (the first option among the four graphs)