Question

Which sequence of transformations produces A’B’C’ from ABC?

On a coordinate plane, triangle A B C has points (3, negative 1), (4, negative 4), (1, negative 2). Triangle A prime B prime C prime has points (negative 2, 3), (1, 4), (negative 1, 1).
a translation up 3 and then a 90º counterclockwise rotation about the origin
a 90º counterclockwise rotation about the origin and then a translation up 3
a reflection over the x-axis and then a translation left 2 and down 1
a translation left 5 and down 2 and then a reflection over the x-axis

Answer 1

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:

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Answer 2

Answer:

A translation up 3 then a 90 degree counterclockwise rotation about the origin.

Step-by-step explanation:

I took the quiz.