Assess parallelograms ADCB and EHGF to decide if they are congruent.
(1 point)
Responses
Yes, ADCB≅EHGF since parallelogram ADCB was translated.
Yes, upper A upper D upper C upper B congruent to upper E upper H upper G upper F since parallelogram upper A upper D upper C upper B was translated.
Yes, ADCB≅EHGF because parallelogram ADCB was rotated.
Yes, upper A upper D upper C upper B congruent to upper E upper H upper G upper F because parallelogram upper A upper D upper C upper B was rotated.
Yes, ADCB≅EHGF because parallelogram ADCB was reflected.
Yes, upper A upper D upper C upper B congruent to upper E upper H upper G upper F because parallelogram upper A upper D upper C upper B was reflected.
No, ADCB is not congruent to EHGF because parallelogram ADCB was dilated.
No, ADCB is not congruent to EHGF because parallelogram ADCB was dilated.
What two rigid transformations were performed on figure ABCD to produce the congruent figure WXYZ?
(1 point)
Responses
ABCD was first shifted 3 units to the left and 5 units up, then rotated −90° (clockwise).
upper A upper B upper C upper D was first shifted 3 units to the left and 5 units up, then rotated negative 90 degrees (clockwise).
ABCD was first shifted 3 units to the left and 5 units up, then rotated 90° (counterclockwise).
upper A upper B upper C upper D was first shifted 3 units to the left and 5 units up, then rotated 90 degrees (counterclockwise).
ABCD was first rotated 90° (counterclockwise), then shifted 3 units to the left and 5 units up.
upper A upper B upper C upper D was first rotated 90 degrees (counterclockwise), then shifted 3 units to the left and 5 units up.
ABCD was first rotated −270° (clockwise), then shifted 3 units to the left and 5 units up.
ABCD was first shifted 3 units to the left and 5 units up, then rotated −90° (clockwise).
Determine the congruence transformation used on △ABC that resulted in △DEF.
(1 point)
Responses
△ABC was reflected across the y-axis, then shifted 2 units to the right and 2 units up.
triangle upper A upper B upper C was reflected across the y -axis, then shifted 2 units to the right and 2 units up.
△ABC was shifted 2 units to the left and 2 units up, then reflected across the y-axis.
triangle upper A upper B upper C was shifted 2 units to the left and 2 units up, then reflected across the y -axis.
△ABC was shifted 2 units to the right and 2 units up, then rotated 180° (counterclockwise).
triangle upper A upper B upper C was shifted 2 units to the right and 2 units up, then rotated 180 degrees (counterclockwise).
△ABC was rotated −180° (clockwise) or 180° (counterclockwise), then shifted 2 units to the right and 2 units up.
△ABC was reflected across the y-axis, then shifted 2 units to the right and 2 units up.
Identify a sequence of rigid transformations that would map ABCD→A"B"C"D". Give your answer in the form of a composition transformation mapping.
(1 point)
Responses
(x,y)→(−x−4,y)
left parenthesis x comma y right parenthesis right arrow left parenthesis negative x minus 4 comma y right parenthesis
(x,y)→(−x,y−4)
left parenthesis x comma y right parenthesis right arrow left parenthesis negative x comma y minus 4 right parenthesis
(x,y)→(x,y+4)
left parenthesis x comma y right parenthesis right arrow left parenthesis x comma y plus 4 right parenthesis
(x,y)→(x,−y−4)
(x,y)→(−x−4,y)
This transformation reflects the figure across the y-axis and then shifts it 4 units to the left.
Identify the sequence of transformations that will carry ΔABC→ΔA"B"C". Give your answer in the form of a composition transformation mapping.
(1 point)
Responses
(x,y)→(x,−y+4)
left parenthesis x comma y right parenthesis right arrow left parenthesis x comma negative y plus 4 right parenthesis
(x,y)→(x,−y−4)
open paren x comma y close paren rightarrow open paren x comma negative y minus 4 close paren
(x,y)→(x+4,−y)
left parenthesis x comma y right parenthesis right arrow left parenthesis x plus 4 comma negative y right parenthesis
(x,y)→(x−4,−y)
(x,y)→(x−4,−y)
This transformation shifts the figure 4 units to the left and reflects it across the x-axis.
To assess whether parallelograms ADCB and EHGF are congruent, you would need to check if they have the same shape and size. Here are the ways to determine congruence:
1. Translation: If ADCB was translated (moved) to form EHGF without any change in shape or size, then ADCB and EHGF would be congruent. The corresponding sides and angles of ADCB would match those of EHGF.
2. Rotation: If ADCB was rotated (turned) to form EHGF without any change in shape or size, then ADCB and EHGF would be congruent. The corresponding sides and angles of ADCB would align with those of EHGF.
3. Reflection: If ADCB was reflected (flipped) to form EHGF without any change in shape or size, then ADCB and EHGF would be congruent. The corresponding sides and angles of ADCB would mirror those of EHGF.
4. Dilation: However, if ADCB was dilated (stretched or shrunk) to form EHGF, they would not be congruent. Congruent figures have the same shape and size, and dilation changes the size.
Based on the provided options, the correct answer would be "No, ADCB is not congruent to EHGF because parallelogram ADCB was dilated." Dilation would change the size of a figure and result in non-congruent parallelograms.