Answer:
The best describes the triangles shown is "triangle 1 and triangle 2 are congruent because triangle 2 can be created by rotating reflecting and translating triangle one"
Step-by-step explanation:
Let us revise some facts about rotation, reflection and translation
- The image of point (x , y) after rotation 90° counterclockwise around the origin is (-y , x)
- The image of point (x , y) after reflection about the y-axis is (-x , y)
- The image of point (x , y) after translation h units to the right is (x + h , k) to the left (x - h, k)
The vertices of triangle 1 are:
(-1 , 4) , (-2 , 8) , (-7 , 5) ⇒ as shown in the figure
If triangle 1 rotates 90° counterclockwise around the origin, change the sign of each y-coordinate and switch the two coordinates of each vertex then the vertices of the new triangle will be:
(-4 , -1) , (-8 , -2) , (-5 , -7)
If the new triangle is reflected about the y-axis, change the sign of x-coordinate of each vertex then the vertices of the new triangle will be:
(4 , -1) , (8 , - 2) , (5 , -7)
If the new triangle is translated 3 units to the left, subtract 3 from the x-coordinate of each vertex then the vertices of triangle 2 are:
(1 , -1) , (5 , -2) , (2 , -7) as the figure shown
Rotation, reflection and translation do not change the size of the shape, so the shape and its image are congruent
Only dilation change the size of the shape, so the shape and its image are similar
The best describes the triangles shown is "triangle 1 and triangle 2 are congruent because triangle 2 can be created by rotating reflecting and translating triangle one"
