The coordinates of P' is (9, -6) and L' is (3, -1).
<h2>
Given that</h2>
PL has endpoints P(4, −6) and L(−2, 1).
The segment is translated using the mapping (x, y) → (x + 5, y).
<h3>
We have to determine</h3>
What are the coordinates of P’ and L’?
<h3>According to the question</h3>
PL has endpoints P(4, −6) and L(−2, 1).
The segment is translated using the mapping (x, y) → (x + 5, y).
The coordinates of point P after translation using mapping is,
![\rm P(x, \ y) - P'(x+5, y)\\ \\ P(4, -6) - P'(4+5, \ -6)\\ \\ P(4, -6) - P'(9, -6)\\](https://tex.z-dn.net/?f=%5Crm%20P%28x%2C%20%5C%20y%29%20-%20P%27%28x%2B5%2C%20y%29%5C%5C%0A%5C%5C%0AP%284%2C%20-6%29%20-%20P%27%284%2B5%2C%20%5C%20-6%29%5C%5C%0A%5C%5C%0AP%284%2C%20-6%29%20-%20P%27%289%2C%20-6%29%5C%5C)
And the coordinates of point L after translation using mapping is,
![\rm L(x, \ y) - L'(x+5, y)\\\\L(-2, 1) - L'(-2+5, \ -1)\\\\L(4, -6) - L'(3, -1)\\](https://tex.z-dn.net/?f=%5Crm%20L%28x%2C%20%5C%20y%29%20-%20L%27%28x%2B5%2C%20y%29%5C%5C%5C%5CL%28-2%2C%201%29%20-%20L%27%28-2%2B5%2C%20%5C%20-1%29%5C%5C%5C%5CL%284%2C%20-6%29%20-%20L%27%283%2C%20-1%29%5C%5C)
Hence, The coordinates of P' is (9, -6) and L' is (3, -1).
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