(x, y) → (x, −y), (x, y) → (x + 1, y + 1) transformation would produce an image with vertices B″(−2, 1), C″(3, 2), D″(0, −1).
A transformation is a process that manipulates a polygon or other two-dimensional object on a plane or coordinate system. Mathematical transformations describe how two-dimensional figures move around a plane or coordinate system.
Given
A triangle has vertices at B(−3, 0), C(2, −1), D(−1, 2).
Option A :
(x, y) → (x, −y), (x, y) → (x + 1, y + 1)
B(-3, 0) ⇒ (-3, -0) = (-3, 0) , (-3, 0) ⇒ (-3 + 1, 0 + 1) = (-2, 1)
Option B :
(x, y) → (−x, y), (x, y) → (x + 1, y + 1)
B(-3, 0) ⇒ (-(-3), 0) = (3, 0) , (3, 0) ⇒ (3 + 1, 0 + 1) = (4, 1)
Option C :
(x, y) → (x, −y), (x, y) → (x + 2, y + 2)
B(-3, 0) ⇒ (-3, -0) = (-3, 0) , (-3, 0) ⇒ (-3 + 2, 0 + 2) = (-1, 2)
Option D :
(x, y) → (−x, y), (x, y) → (x + 2, y + 2)
B(-3, 0) ⇒ (-(-3), 0) = (3, 0) , (3, 0) ⇒ (3 + 2, 0 + 2) = (5, 2)
So, (x, y) → (x, −y), (x, y) → (x + 1, y + 1) transformation would produce an image with vertices B″(−2, 1), C″(3, 2), D″(0, −1).
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