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Mathematics

1 answer:

motikmotik2 years ago

6 0

Answer:

Step-by-step explanation:

A coordinate grid is shown from negative 5 to 0 to 5 on both x- and y-axes. A polygon ABCD has A at ordered pair (2, 3), B at ordered pair (4, 4), C at ordered pair (3, 1), D at ordered pair (2, 1). A polygon A'B'C'D' has A' at ordered pair (-1, 3), B' at ordered pair (-3, 4), C' at ordered pair (-2, 1), D' at ordered pair (-1, 1).

Which of the following sequences of transformations is used to obtain figure A'B'C'D' from figure ABCD? (1 point)

a ) Counterclockwise rotation by 90 degrees about the origin followed by a translation to the right by 1 unit

b) Counterclockwise rotation by 90 degrees about the origin followed by a translation to the left by 1 unit

c ) Reflection about the x-axis followed by a translation to the left by 1 unit

d ) Reflection about the y-axis followed by a translation to the right by 1 unit

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Help!! I'll give points if anybody can answer these for me!

galina1969 [7]

Transformation involves changing the position of a shape.

The transformation from $\triangle ABC$ to $\triangle A'B'C'$ is 90 degrees clockwise rotation

Using the coordinates of A and A', we have:

$A= (-6,3)$

$A'= (3,6)$

Notice that the x-coordinate is negated and then swapped with the y-coordinate.

i.e.

$(x,y) \to (y,-x)$

The transformation of a point from (x,y) to (y,-x) is a 90 degrees clockwise rotation.

Hence, the transformation from $\triangle ABC$ to $\triangle A'B'C'$ is 90 degrees clockwise rotation