Pythagorean Theorem
Which measurements could represent the side lengths in inches of a right triangle?
A. 5 in., 5 in., 50 in.
B. 16 in., 16 in., 16 in.
C. 7 in., 8 in., 15 in.
D. 16 in., 30 in., 34 in.
D. 16 in., 30 in., 34 in.
Triangle MNO on a coordinate grid is rotated 90 degrees clockwise around the origin to create triangle M'N'O'. Which of the following rules describes this transformation?
A. (x,y) -> (y,-x)
B. (x,y) -> (-y,x)
C. (x,y) -> (-x,y)
D. (x,y) -> (x,-y)
A. (x,y) -> (y,-x)
Quadrilateral JKLM was translated 5 units to the right, and 3 units up to create quadrilateral J'K'L'M'. Which rule describes this transformation?
A. (x,y) -> (x - 5, y - 3)
B. (x,y) -> (x + 5, y + 3)
C. (x,y) -> (x - 3, y - 5)
D. (x,y) -> (x + 3, y + 5)
B. (x,y) -> (x + 5, y + 3)
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. (x,y) -> (0.5 - x, 0.5 - y)
B. (x,y) -> (x - 7, y - 7)
C. (x,y) -> (5/4x, 5/4y)
D. (x,y) -> (0.9x, 0.9y)
D. (x,y) -> (0.9x, 0.9y)
Pentagon VWXYZ is shown on the coordinate grid. A student reflected pentagon VWXYZ across the x-axis to create pentagon V'W'X'Y'Z'.
Which rule describes this transformation?
A. (x,y) -> (x,-y)
B. (x,y) -> (x, y + 8)
C. (x,y) -> (-y,x)
D. (x,y) -> (-x,y)
A. (x,y) -> (x,-y)
Which measurement could represent the side lengths in feet of a right triangle?
A. 10 ft, 24 ft, 26 ft
B. 14 ft, 14 ft, 14 ft
C. 3 ft, 3 ft, 18 ft
D. 2 ft, 3 ft, 5 ft
A. 10 ft, 24 ft, 26 ft
Square ABCD on a coordinate grid is rotated 270 degrees clockwise around the origin to create square A'B'C'D'. Which of the following rules describes this transformation?
A. (x,y) -> (x,-y)
B. (x,y) -> (-y,x)
C. (x,y) -> (-x,y)
D. (x,y) -> (y,-x)
B. (x,y) -> (-y,x)
Trapezoid WKRP was translated 4 units to the left and 5 units up on a coordinate grid to create trapezoid W'K'R'P'. Which rule describes this transformation?
A. (x,y) -> (x - 4, y + 5)
B. (x,y) -> (x + 4, y - 5)
C. (x,y) -> (x + 4, y + 5)
D. (x,y) -> (x - 4, y - 5)
A. (x,y) -> (x - 4, y + 5)
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?
A. If a is greater than 1, the image of the polygon is congruent to the polygon.
B. If a is between 0 and 1, the image of the polygon is congruent to the polygon.
C. If a is greater than 1, the image of the polygon is smaller than the polygon.
D. If a is between 0 and 1, the image of the polygon is
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?
A. If a is greater than 1, the image of the polygon is congruent to the polygon.
B. If a is between 0 and 1, the image of the polygon is congruent to the polygon.
C. If a is greater than 1, the image of the polygon is smaller than the polygon.
D. If a is between 0 and 1, the image of the polygon is smaller than the polygon.
D. If a is between 0 and 1, the image of the polygon is smaller than the polygon.
Quadrilateral PQRS is reflected across the x-axis to create quadrilateral P'Q'R'S'. Which one of the following rules describes this transformation?
A. (x,y) -> (-y,x)
B. (x,y) -> (x,y)
C. (x,y) -> (x,-y)
D. (x,y) -> (y,-x)
C. (x,y) -> (x,-y)
The width of a rectangle is 4 feet, and the diagonal length of the rectangle is 13 feet. Which measurement is closest to the length of this rectangle in feet?
A. 9 ft
B. 17 ft
C. 12.4 ft
D. 13.6 ft
D. 13.6 ft
A figure on a coordinate plane is rotated 180 degrees counterclockwise around the origin to create a new figure. Which one of the following rules describes this transformation?
A. (x,y) -> (-x,-y)
B. (x,y) -> (x,y)
C. (x,y) -> (-x,y)
D. (x,y) -> (x,-y)
A. (x,y) -> (-x,-y)
Triangle ABC was translated 2 units to the right and 3 units down. Which rule describes the translation that was applied to triangle ABC to create triangle A'B'C'?
A. (x,y) -> (x - 3, y + 2)
B. (x,y) -> (x + 2, y - 3)
C. (x,y) -> (2x,-3y)
D. (x,y) -> (-3x,2y)
B. (x,y) -> (x + 2, y - 3)
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'?
A. (6 + u, -3 + u)
B. (6/u, - 3/u)
C. (6 + 1/u, -3 + 1/u)
D. (6u, -3u)
D. (6u, -3u)
Triangle MNO on a coordinate plane is reflected across the x-axis to create triangle M'N'O'. Which one of the following rules describes this transformation?
A. (x,y) -> (-x,y)
B. (x,y) -> (x,-y)
C. (x,y) -> (-y,x)
D. (x,y) -> (y,-x)
B. (x,y) -> (x,-y)
The dimensions of a rectangular piece of paper are 8.5 inches and 11 inches. Veronica folded the piece of paper along its diagonal. Which measurement is closest to the length of the diagonal in inches?
A. 6.24 in.
B. 19.5 in.
C. 6.98 in.
D. 13.9 in.
D. 13.9 in.
Parallelogram PQRS is rotated 90 degrees clockwise around the origin to create parallelogram P'Q'R'S'. Which rule describes this transformation?
A. (x,y) -> (x,-y)
B. (x,y) -> (-x,y)
C. (x,y) -> (y,x)
D. (x,y) -> (y,-x)
D. (x,y) -> (y,-x)
Triangle MNO on a coordinate plane is translated 6 units up to create triangle M'N'O'. Which one of the following rules describes this transformation?
A. (x,y) -> (x - 6, y)
B. (x,y) -> (x, y - 6)
C. (x,y) -> (x + 6, y)
D. (x,y) -> (x, y + 6)
D. (x,y) -> (x, y + 6)
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 with 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?
A. (20x, 20y)
B. (0.4x, 0.4y)
C. (x + 20, y + 20)
D. (x + 0.4, y + 0.4)
B. (0.4x, 0.4y)
A figure on a coordinate plane is reflected across the x-axis to create a new figure. Which of the following rules describes this transformation?
A. (x,y) -> (x,y)
B. (x,y) -> (-x,-y)
C. (x,y) -> (-x,y)
D. (x,y) -> (x,-y)
D. (x,y) -> (x,-y)
The length of a rectangular frame is 15 inches, and the width of the frame is 8 inches. What is the length of a diagonal of this frame in inches?
17 inches
Quadrilateral PQRS is rotated 360 degrees counterclockwise around the origin to create quadrilateral P'Q'R'S'. Which one of the following rules describes this transformation?
A. (x,y) -> (-x,y)
B. (x,y) -> (x,-y)
C. (x,y) -> (x,y)
D. (x,y) -> (-y,x)
C. (x,y) -> (x,y)
A circle is graphed on a coordinate grid with its center at (-4,7). The circle will be translated p units to the right and v units down. Which rule describes the center of the new circle after this translation?
A. (x,y) -> (- 4 + p, 7 + v)
B. (x,y) -> (- 4 + p, 7 - v)
C. (x,y) -> (- 4 - p)
D. (x,y) -> (y,-x)
B. (x,y) -> (- 4 + p, 7 - v)
A rectangle will be dilated on a coordinate grid to create a larger rectangle. The rectangle is dilated using the origin as the center of dilation.
Which rule could represent this dilation?
A. (x,y) -> (0.88x, 0.88y)
B. (x,y) -> (10/9x, 10/9y)
C. (x,y) -> (1.25 + x, 1.25 + y)
D. (x,y) -> (x - 1/4, y - 1/4)
B. (x,y) -> (10/9x, 10/9y)
Triangle MNO on a coordinate plane is reflected across the y-axis to create triangle M'N'O'. Which one of the following rules describes this transformation?
A. (x,y) -> (-x,y)
B. (x,y) -> (x,-y)
C. (x,y) -> (-y,x)
D. (x,y) -> (y,-x)
A. (x,y) -> (-x,y)