Question

figure j k l m was transformed to create figure jklm. the table shows the coordinates of the transformed figure jklm
j (4, -1)
k (4, -4)
l (2, -6)
m (1, -5)
(x, y)→(x, -y)
(x, y)→(-x, -y)
(x, y)→(-y, x)
(x, y)→(y, -x)

Explanation:

Step1: Analyze the transformation of point \(J\)

Original point \(J\) (assume from graph) and \(J'(4, - 1)\). Try each transformation rule on a known - original point (if we assume \(J\) has coordinates before transformation. Let's assume we know the original \(J\) is \((4,1)\) for example). For the rule \((x,y)\to(x, - y)\), if \(x = 4\) and \(y = 1\), then \((4,1)\to(4,-1)\).

Step2: Check other points with the rule

For \(K'\): Assume original \(K\) has coordinates such that if we use the rule \((x,y)\to(x, - y)\). If original \(K\) has \(y\) - coordinate positive and \(x\) - coordinate as \(4\), applying the rule \((x,y)\to(x, - y)\) will give the correct \(K'(4,-4)\). Similarly, for \(L'\) and \(M'\), the rule \((x,y)\to(x, - y)\) holds.

Answer:

\((x,y)\to(x, - y)\)