Question

after examining the following graph, joe claims that the figure m is translated to figure l according to the rule (x, y) -> (x + 1,y + 4). is she correct?
no. figure m to figure l is translated by the rule (x, y) -> (x + 1,y - 4).
no. figure m to figure l is translated by the rule (x, y) -> (y + 1,x - 4).

Explanation:

Step1: Check x - coordinate change

Pick a vertex of figure M, say the left - most vertex of figure M which is at (-4, 4). According to the rule \((x,y)\to(x + 1,y+4)\), the x - coordinate of the new point should be \(x=-4 + 1=-3\). But looking at the corresponding vertex in figure L, the x - coordinate of the left - most vertex of figure L is \(-3\).

Step2: Check y - coordinate change

For the same vertex of figure M at (-4, 4), according to the rule \((x,y)\to(x + 1,y + 4)\), the y - coordinate of the new point should be \(y=4 + 4 = 8\). But the y - coordinate of the corresponding vertex in figure L is \(0\). The actual change in y - coordinate from figure M to figure L for this vertex is \(4-0 = 4\) in the negative direction. The correct rule for translation from figure M to figure L for x - coordinate is \(x\to x + 1\) and for y - coordinate is \(y\to y-4\), i.e., the rule is \((x,y)\to(x + 1,y - 4)\).

Answer:

No, figure M to figure L is translated by the rule \((x,y)\to(x + 1,y - 4)\)