Question

The endpoints of bar (PQ) are P(-4,6) and Q(3,-7). Find the endpoints of the image of bar (PQ) after the composition. Translation: (x,y)->(x-8,y) Translation: (x,y)->(x+1,y+6)

Answer 1

The endpoints of the image of bar PQ after the composition of the given translations are P'(-11, 12) and Q'(-4, -1).

Step-by-step explanation:

To find the endpoints of the image of bar PQ after the composition of the given translations, we need to perform each translation separately and then combine the results.

Translation (x,y) -> (x-8,y) moves each point horizontally 8 units to the left, while keeping the y-coordinate the same. So, the image of P after this translation is (-4-8, 6) = (-12, 6) and the image of Q is (3-8, -7) = (-5, -7).

Translation (x,y) -> (x+1,y+6) moves each point horizontally 1 unit to the right and vertically 6 units up. So, the image of (-12, 6) after this translation is (-12+1, 6+6) = (-11, 12) and the image of (-5, -7) is (-5+1, -7+6) = (-4, -1).

Therefore, the endpoints of the image of bar PQ after the composition of the given translations are P'(-11, 12) and Q'(-4, -1).