Question

what is the rule for this translation? (x, y) --> (x+5, y-3) (x, y) --> (x-4, y-6) (x, y) --> (x+6, y-4)

Explanation:

Step1: Observe x - coordinate change

Pick a vertex of the original triangle. Let's assume its x - coordinate is \(x\). After translation, if the new x - coordinate is \(x + a\), \(a\) is the horizontal shift. If the new x - coordinate is \(x - a\), it shifts left by \(a\) units.

Step2: Observe y - coordinate change

Pick the same vertex. If its original y - coordinate is \(y\) and the new y - coordinate is \(y + b\), it shifts up by \(b\) units. If the new y - coordinate is \(y - b\), it shifts down by \(b\) units.

Step3: Analyze the options

For option \((x,y)\to(x + 5,y - 3)\), it means a right - shift of 5 units and a down - shift of 3 units. For option \((x,y)\to(x - 4,y - 6)\), it means a left - shift of 4 units and a down - shift of 6 units. For option \((x,y)\to(x + 6,y - 4)\), it means a right - shift of 6 units and a down - shift of 4 units. By visually inspecting the graph, we can see that the triangle moves right and down. If we count the grid squares for a particular vertex (say the top - left vertex of the blue triangle to its corresponding vertex on the red triangle), we find that it moves 5 units to the right and 3 units down.

Answer:

\((x,y)\to(x + 5,y - 3)\)