The sequence of transformations produces A’B’C’ from ABC is " a translation up 3 and then a 90° counterclockwise rotation about the origin " ⇒ 1st answer
Step-by-step explanation:
Let us revise some transformation of a point
- If the point (x , y) translated vertically up by k units then its image is (x , y + k)
- If the point (x , y) translated vertically down by k units then its image is (x , y - k)
- If point (x , y) rotated about the origin by angle 90° counterclockwise, then its image is (-y , x)
- If point (x , y) rotated about the origin by angle 180° counterclockwise, then its image is (-x , -y)
- If point (x , y) rotated about the origin by angle 270° counterclockwise, then its image is (y , -x)
∵ The vertices of triangle ABC are (3 , -1), (4 , -4), (1 , -2)
- If the triangle translated 3 units up, then add 3 to the
y-coordinate of each vertex
∴ the new vertices are (3 , -1 + 3), (4 , -4 + 3), (1 , -2 + 3)
∴ the new vertices are (3 , 2), (4 , -1), (1 , 1)
- If then rotated 90° counterclockwise around the origin, then
change the sign of the y-coordinate of each vertex and switch
the two coordinates
∵ The y-coordinates are 2, -1, 1
- Change their signs
∴ The new y-coordinates are -2, 1, -1
- Switch the coordinates
∴ The new vertices are (-2 , 3) , (1 , 4), (-1 , 1)
∵ The vertices of triangle A'B'C' are (-2 , 3), (1 , 4), (-1 , 1)
∴ ΔABC is translated up 3 units and rotated around the origin
counterclockwise 90°
The sequence of transformations produces A’B’C’ from ABC is "a translation up 3 and then a 90° counterclockwise rotation about the origin"
Learn more:
You can learn more about the transformation in brainly.com/question/9381523
#LearnwithBrainly
