Question

100 points! PLEASE HELP!

Describe the transformations that occurred: (Write your original points, show your work for each transformation, and then highlight your transformations.) A(-3,1) B(-4,5) A'( ) A"(0,-4) B'( ) B"( 1,0 ) C(-1,3 ) C'( ) C"(-2,-2)​

Answer 1

Answer:

Reflection across the y-axis: A'(3, 1), B'(4, 5), C'(1, 3)

Translation of 3 units left and 5 units down: A''(0, -4), B''(1, 0), C''(-2, -2)

Step-by-step explanation:

To map triangle ABC to triangle A''B''C'', we can first reflect ΔABC in the y-axis to obtain ΔA'B'C', and then translate ΔA'B'C' 3 units left and 5 units down to get ΔA''B''C''.

Transformation 1: Reflection across the y-axis

When a figure is reflected across the y-axis, the x-coordinate of each point is negated and the y-coordinate remains unchanged:

$(x,y)\rightarrow (-x,y)$

Therefore, when triangle ABC is reflected across the y-axis, the coordinates of its vertices become:

• A'(3, 1)
• B'(4, 5)
• C'(1, 3)

Transformation 2: Translation of 3 units left and 5 units down

When a figure is translated 3 units left, we subtract 3 from its x-coordinate. When a figure is translated 5 units down, we subtract 5 from its y-coordinate:

$(x,y)\rightarrow (x-3,y-5)$

Therefore, when triangle A'B'C' is translated 3 units left and 5 units down, the coordinates of its vertices become:

• A'' = (3-3, 1-5) = (0, -4)
• B'' = (4-3, 5-5) = (1, 0)
• C'' = (1-3, 3-5) = (-2, -2)