Question

the graph shows the location of the entrance to a state park. each unit on the graph represents 1 kilometer. rodrigo uses the graph to locate a waterfall. the waterfall is located 3 kilometers to the left and 4 kilometers down from the park entrance. rodrigo says the ordered pair for the waterfall is (3, 9). use the drop - down menus to explain rodrigo’s error.

Explanation:

Step1: Identify Park Entrance Coordinates

Assume park entrance is at \((x_0, y_0)\). From graph, estimate park entrance (e.g., if park entrance is at \((6, 6)\) (visually, middle - right, middle - y)).

Step2: Analyze Left and Down Movements

• Moving left: decreases \(x\)-coordinate. 3 km left: \(x = x_0-3\).
• Moving down: decreases \(y\)-coordinate. 4 km down: \(y = y_0 - 4\).
• If park entrance is \((6,6)\), then correct coordinates: \(x=6 - 3=3\), \(y = 6-4 = 2\), so \((3,2)\).
• Rodrigo's error: He increased \(y\) (used 9 instead of \(6 - 4 = 2\)) and likely mixed up direction (down should decrease \(y\), he might have increased or miscalculated \(y\) - coordinate). Also, ordered pairs are \((x,y)\), left affects \(x\) (decrease), down affects \(y\) (decrease). Rodrigo probably added to \(y\) instead of subtracting or misassigned the direction of movement to the wrong coordinate.

Answer:

Rodrigo's error is that when moving down (which affects the \(y\)-coordinate), he should subtract 4 from the park entrance's \(y\)-coordinate, but he likely added or miscalculated, and for the \(x\)-coordinate (moving left subtracts from \(x\), which he did correctly as \(x = 6-3 = 3\) if entrance is \((6,6)\), but messed up \(y\) (should be \(6 - 4=2\) not 9). So the correct ordered pair should be \((3,2)\) (depending on entrance coordinates), and Rodrigo incorrectly calculated the \(y\)-coordinate by not subtracting the downward distance (or adding instead) and messed up the \(y\)-value.