Staar Released Questions Over Transformations

Pentagon MNPQR is shown on the coordinate grid. Pentagon MNPQR is dilated using the rule (x, y)→(1/4x, 1/4y) to create pentagon M'N'P'Q'R'. Which statement is true?

• Pentagon M'N'P'Q'R' is larger than pentagon MNPQR, because the scale factor is greater than 1.

• Pentagon M'N'P'Q'R' is smaller than pentagon MNPQR, because the scale factor is less than 1.

• Pentagon M'N'P'Q'R' is smaller than pentagon MNPQR, because the scale factor is greater than 1.

• Pentagon M'N'P'Q'R' is larger than pentagon MNPQR, because the scale factor is less than 1.

A polygon will be dilated on a coordinate grid to create a smaller polygon. The polygon is dilated using the origin as the center of dilation. Which rule could represent this dilation?

• 
• 
• 
• 

A polygon is graphed on a coordinate grid with (x,y) representing the location of a certain point on the polygon. The polygon is transformed using the rule (x, y)→(ax, ay). Which statement must be true?

• If a is greater than 1, the image of the polygon is congruent to the polygon.

• If a is between 0 and 1, the image of the polygon is congruent to the polygon.

• If a is greater than 1, the image of the polygon is smaller than the polygon.

• If a is between 0 and 1, the image of the polygon is smaller than the polygon.

Triangle JKL is dilated with the origin as the center of dilation to create J'K'L'. Which rule best represents the dilation that has been applied to triangle JKL to create triangle J'K'L'?

• 
• 
• 
• 

A square with a perimeter of 20 units is graphed on a coordinate grid. The square is dilated by a scale factor of 0.4 which the origin as the center of dilation. If (x,y) represents the location of any point on the original square, which ordered pair represents the coordinates of the corresponding point on the resulting square?

• (20x, 20y)

• (0.4x, 0.4y)

• (x+20, y+20)

• (x+0.4, y+0.4)

Triangle MNP is graphed on a coordinate grid with vertices at M(-3,-6), N(0,3) and P(6,-3). Triangle MNP is dilated by a scale factor of u with the origin as the center of dilation to create triangle M'N'P'. Which ordered pair represents the coordinates of the vertex P'?

• (6+u, -3+u)

• (6/u, -3/u)

• (6+1/u, -3+1/u)

• (6u, -3u)

Circle I is dilated to create Circle II.  Which could be the scale factor of the dilation?

• 5
• 3/8
• 8
• 8/3

Figure S is dilated to create Figure T.  Which could be the scale factor of the dilation?

• (x, y)→(2x, 2y)
• (x, y)→(1/2 x, 1/2 y)
• (x, y)→(3x, 3y)
• (x, y)→(4x, 6y)

Which representation of a transformation on a coordinate grid does NOT preserve congruence?

• (x, y)→(1/7x, 1/7y)

• (x, y)→(x+7, y+7)

• (x, y)→(x, -y)

• (x, y)→(y, -x)

Quadrilateral PQRS was translated 5 units to the right and 3 units up to create quadrilateral P'Q'R'S'. Which rule describes this transformation?

• (x, y)→(x-5, y-3)

• (x, y)→(x+5, y+3)

• (x, y)→(x-3, y-5)

• (x, y)→(x+3, y+5)