Question

1. a triangle with vertices (1,1), (3,1), (2,4) is translated using the rule (x - 2,y + 2). what are the new coordinates of the triangle?

a) (-1,3), (1,3), (0,6)
b) (3,3), (5,3), (4,6)
c) (-1,-1), (1,-1), (0,2)
d) (2,2), (4,2), (3,5)

1. which transformation always produces a congruent figure?

a) reflection
b) rotation
c) translation
d) all of the above

Explanation:

planation:

Step1: Apply translation rule to first vertex

For vertex $(1,1)$, using the rule $(x - 2,y + 2)$, we have $x=1,y = 1$. New $x=1 - 2=-1$, new $y=1 + 2 = 3$. So new vertex is $(-1,3)$.

Step2: Apply translation rule to second vertex

For vertex $(3,1)$, with $x = 3,y = 1$. New $x=3 - 2=1$, new $y=1 + 2 = 3$. So new vertex is $(1,3)$.

Step3: Apply translation rule to third vertex

For vertex $(2,4)$, with $x = 2,y = 4$. New $x=2 - 2=0$, new $y=4 + 2 = 6$. So new vertex is $(0,6)$.

For question 12:

• Reflection, rotation and translation are all rigid - motions. Rigid - motions preserve the shape and size of a figure, which means they produce congruent figures.

Answer:

1. A. $(-1,3),(1,3),(0,6)$
2. D. All of the above