Final answer:
The triangle with vertices a(1,0), b(0,1), c(1,1) is first rotated 450 degrees about the origin (which is effectively a 90 degree rotation), resulting in a'(-1,1), b'(-1,0) and c'(-1,1). These points are then translated 2 units in both x and y directions, resulting in final vertices a''(1,3), b''(1,2), and c''(1,3).
Step-by-step explanation:
The question asks for a two-step transformation of a triangle with vertices at points a(1,0), b(0,1), and c(1,1). The steps are a rotation of 450 degrees about the origin, followed by a translation in both the x and y directions.
First, remember that in a rotation, a point (x,y) rotates to a new point (x',y') according to the formula x' = x * cos(θ) - y * sin(θ) and y' = x * sin(θ) + y * cos(θ), where θ is the given angle of rotation.
We use θ = 450°, but since a full rotation is 360°, it is as if we are rotating only 90°,
so cos(90°) = 0 and sin(90°) = 1.
The new rotated points will be a'(-1,1), b'(-1,0) and c'(-1,1).
The translation moves every point a fixed distance in a specific direction. It changes the x-coordinate and y-coordinate by the same values. In this question, it tells us to move 2 units in both x and y direction, so each point's new coordinates will be raised by 2.
After this transformation, our final points for the triangle will be a''(1,3), b''(1,2), and c''(1,3).
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