Question

wednesday
in what direction will this arrow point after it is rotated 270° counterclockwise?
arrow image
thursday
draw the figure below after a 90° counter - clockwise rotation.
figure image
which transformations will not result in a congruent figure?
a) rotation
b) reflection
c) translation
d) dilation
under a dilation, triangle a(0,0), b(0,4), c(6,0) becomes triangle a(0,0), b(0,10), c(15,0). what is the scale factor for this dilation?

Explanation:

Step1: Rotate arrow 270° counterclockwise

A 270° counterclockwise rotation is equivalent to a 90° clockwise rotation. An arrow pointing left (west) rotated 90° clockwise will point down (south).

Step2: Identify non-congruent transformation

Congruent figures have equal size/shape. Rotation, reflection, translation preserve size; dilation changes size.

Step3: Calculate dilation scale factor

Use corresponding coordinates: $\text{Scale factor} = \frac{\text{New coordinate}}{\text{Original coordinate}}$. For point B: $\frac{10}{4} = 2.5$; for point C: $\frac{15}{6} = 2.5$.

Step4: Rotate net 90° counterclockwise

Rotate each square 90° counterclockwise around a central point: the top square moves to the left of the first square in the main row, the bottom square moves to the right of the last square in the main row, and the main row shifts accordingly.

Answer:

1. The arrow will point downward (south).
2. (Rotated net: a 5-square net where the top square is now to the left of the first square in the horizontal row, the bottom square is to the right of the last square in the horizontal row, and the horizontal row remains 3 squares long, with the left square having a square above it and the right square having a square below it in the rotated orientation)
3. D) Dilation
4. $2.5$ (or $\frac{5}{2}$)