Euclidean geometry: transformations and congruence

High School Math 1 · Unit 16 · transformations-congruence

transformations-congruence

Name ______________________________Date ______________

1.
The point $(3, -2)$ is rotated $90^\circ$ counter-clockwise about the origin. Enter the $x$ -coordinate of the image.
Answer: ______________
2.
A vertex $P(-4, 6)$ of a triangle is rotated $90^\circ$ counter-clockwise about the origin, and the result is then dilated by a scale factor of $\dfrac{1}{2}$ about the origin. Enter the $y$ -coordinate of the final image.
Answer: ______________
3.
A single transformation maps $A(2, 5)$ to $A'(5, 2)$ and $B(-1, 3)$ to $B'(3, -1)$ . Which transformation is it?
1. (A)
  Reflection over the $x$ -axis
2. (B)
  Rotation of $90^\circ$ counter-clockwise about the origin
3. (C)
  Translation by $(3, -3)$
4. (D)
  Reflection over the line $y = x$
4.
Two triangles share some equal measurements. Which set of equal parts guarantees the triangles are congruent?
1. (A)
  Two sides and a non-included angle
2. (B)
  Three angles
3. (C)
  Two sides and the included angle
4. (D)
  One side and one angle
5.
A triangle has vertices $(1, 1)$ , $(5, 1)$ , and $(1, 4)$ . It is dilated by a scale factor of $3$ about the origin. What is the perimeter of the image, in units?
Answer: ______________