DCA 5 Corrections

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

• (x, y) → (x + 6, y – 3)

• (x, y) → (x + 4.5, y + 3)

The length of a rectangular frame is 15 inches, and the width of the frame is 8 inches. What is the length of the diagonal of this frame in inches?

• 17 inches

• 15 inches

• 20 inches

• 25 inches

In the diagram below, RSTU is a rectangle, and the two shaded regions are squares. If the length of UP is 4 meters and the length of UQ is 8 meters, what is the length of PQ in meters?

Ryan transforms rectangle LMNO using the algebraic rule (x, y) → (-x, y). Which transformation did Ryan perform?

• Translation

• Reflection over the y-axis

• Rotation

• Reflection over the x-axis

Answer explanation

Ryan's transformation rule (x, y) → (-x, y) indicates that the x-coordinates are negated while the y-coordinates remain unchanged. This describes a reflection over the y-axis, making it the correct choice.

A 10-foot ladder is leaning against a wall. The bottom of the ladder is 4 feet from the base of the wall. Which of the following is closest to the distance from the top of the ladder to the base of the wall?

• 6 ft.

• 9 ft.

• 11 ft.

• 14 ft.

The coordinate grid shows a pentagon. The pentagon is translated 1 unit to the left and 10 units down to create a new pentagon. Which rule describes this transformation?

• (x, y) → (x - 1, y - 10)

• (x, y) → (x + 1, y - 10)

• (x, y) → (x - 1, y + 10)

• (x, y) → (x + 1, y + 10)

Answer explanation

The transformation translates the pentagon 1 unit left (subtracting 1 from x) and 10 units down (subtracting 10 from y). Thus, the correct rule is (x, y) → (x - 1, y - 10).

A square is dilated by a scale factor 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 of the new square?

• (20x, 20y)

• (0.4x, 0.4y)

• (x + 20, y + 20)

• (x + 0.4, y + 0.4)

Answer explanation

When a square is dilated by a scale factor of 0.4, each coordinate (x, y) of the original square is multiplied by 0.4. Thus, the new coordinates are (0.4x, 0.4y), making (0.4x, 0.4y) the correct choice.

Quadrilateral KITS was dilated with the origin as the center of dilation to create quadrilateral K’I’T’S’. Which of the following rules describes the dilation?

A rectangle is graphed on a coordinate grid. Which transformation will result in a rectangle that is NOT congruent to the original rectangle?

• A. A translation 90 units to the right.

• B. A rotation 180° counterclockwise.

• C. A dilation by a scale factor of 3.

• D. A reflection across the x-axis.

Answer explanation

A dilation by a scale factor of 3 changes the size of the rectangle, making it larger and not congruent to the original. The other transformations (translation, rotation, reflection) preserve congruence.

Parallelogram PQRS is rotated 90° clockwise about the origin to create parallelogram P’Q’R’S’. Which Algebraic Rule represents the rotation?

Answer explanation

A 90° clockwise rotation transforms the point 1 turn to the right. Thus, the correct algebraic rule for this rotation is (x, y) → (y, -x).