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Polygons QRST and Q′R′S′T′ are shown on the following coordinate grid:

A coordinate plane with two polygons is shown. Polygon QRST has vertices Q at 3 comma negative 5, R at 2 comma negative 1, S at 5 comma 0, and T at 5 comma negative 4. Polygon Q prime R prime S prime T prime has vertices at Q prime negative 5 comma negative 4, R prime at negative 1 comma negative 3, S prime at 0 comma negative 6, and T prime at negative 4 comma negative 6.

What set of transformations is performed on QRST to form Q′R′S′T′?

A 180-degree clockwise rotation about the origin followed by a translation 1 unit to the right
A 180-degree clockwise rotation about the origin followed by a translation 1 unit to the left
A translation 1 unit to the left followed by a 270-degree counterclockwise rotation about the origin
A translation 1 unit to the right followed by a 270-degree counterclockwise rotation about the origin

Respuesta :

mhanifa

Answer:

  • D. A translation 1 unit to the right followed by a 270-degree counterclockwise rotation about the origin

Step-by-step explanation:

See the picture for better visual

Take segments ST and S'T'. If we extend them they will intersect at right angle.

It is the indication that the rotation is 90° or 270° but not 180°, when the corresponding segments come parallel.

The QRST is in the quadrant IV and Q'R'S'T' is in the quadrant III, which mean the rotation is 90° clockwise or 270° counterclockwise.

This rotation rule is:

  • (x, y) → (y, -x)

We also see the points S and T have x-coordinate of 5 but their images have y-coordinates of -6. It means the translation to the right by 1 unit was the step before rotation.

We now can conclude the correct choice is D:

  • A translation 1 unit to the right followed by a 270-degree counterclockwise rotation about the origin
Ver imagen mhanifa