Question

pl has endpoints p (4, -6) and l (-2, 1).
the segment is translated using the mapping (x, y) → (x + 5, y).
what are the coordinates of p and l?
p(4, -6),
l(3, 1)
p(9, -1),
l(3, 6)
p(9, -6),
l(-2, 1)
p(9, -6),
l(3, 1)

Explanation:

Step1: Apply the translation rule to point \(P\)

The translation rule is \((x,y)\to(x + 5,y)\). For point \(P(4,-6)\), substitute \(x = 4\) and \(y=-6\) into the rule.
The \(x\) - coordinate of \(P'\) is \(4+5=9\), and the \(y\) - coordinate of \(P'\) is \(-6\). So \(P'=(9,-6)\)

Step2: Apply the translation rule to point \(L\)

For point \(L(-2,1)\), substitute \(x=-2\) and \(y = 1\) into the rule \((x,y)\to(x + 5,y)\)
The \(x\) - coordinate of \(L'\) is \(-2 + 5=3\), and the \(y\) - coordinate of \(L'\) is \(1\). So \(L'=(3,1)\)

Answer:

\(P'(9,-6)\) and \(L'(3,1)\)