Question

error analysis describe and correct the error in graphing the image of quadrilateral efgh after the translation (x, y) → (x − 1, y − 2). 8.

Explanation:

Step1: Analyze Translation Rule

The translation rule is \((x, y) \to (x - 1, y - 2)\), meaning each point should move 1 unit left (subtract 1 from \(x\)-coordinate) and 2 units down (subtract 2 from \(y\)-coordinate).

Step2: Check Each Point

• For point \(F\): Let's assume \(F\) has coordinates (say, from graph) \(F(8, 3)\). Applying translation: \(x - 1 = 8 - 1 = 7\), \(y - 2 = 3 - 2 = 1\). But in the graph, \(F'\) is at \((8, 4)\) (wrong, moved up instead of down).
• For point \(G\): Assume \(G(7, 0)\). Translation: \(x - 1 = 6\), \(y - 2 = - 2\). But \(G'\) is at \((8, 1)\) (wrong, moved right and up).
• Correct approach: For each vertex \(E, F, G, H\), apply \((x - 1, y - 2)\) correctly. For example, if \(E(3, 2)\), then \(E'(3 - 1, 2 - 2)=(2, 0)\); \(F(8, 3)\to F'(7, 1)\); \(G(7, 0)\to G'(6, - 2)\); \(H(4, 1)\to H'(3, - 1)\). Then connect these correct image points.

Answer:

The error is that the translation was not applied correctly to all points (e.g., \(F\) and \(G\) were moved incorrectly: \(F\) was moved up instead of down, \(G\) was moved right and up instead of left and down). To correct, apply \((x,y)\to(x - 1,y - 2)\) to each vertex of \(EFGH\): subtract 1 from each \(x\)-coordinate and 2 from each \(y\)-coordinate, then graph the new vertices and connect them.