Which transformation or series of transformations would prove that XYZ is congruent to QRS? Select yes or no for each transforma
tion or series transformation.
Rotation 90 clockwise about origin {Yes or No}
Translation 9 unit right and 2 units down {Yes or No}
Reflection the y-axis ,followed by a translation 2 units down {Yes or No}
Reflection the x-axis followed by a reflection in the y-axis {Yes or No}
Translation 2 units down and 2 units right, followed by a reflection in the line x=1 Yes or no
Rotation 90 clockwise about origin {Yes or No}
Translation 9 unit right and 2 units down {Yes or No}
Reflection the y-axis ,followed by a translation 2 units down {Yes or No}
Reflection the x-axis followed by a reflection in the y-axis {Yes or No}
Translation 2 units down and 2 units right, followed by a reflection in the line x=1 Yes or no
1 answer:
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Let's write the general form of the sine curve:
, where,
- A is the amplitude. Also, if A is negative, curve reflects about x axis
- B is the compression/stretching factor. It changes the period when it is a value other than 1.
- C is the phase shift. It translates curve left or right. Negative value shifts right and positive value shifts left.
- D is the vertical shift. It translates curve up or down. Negative value shifts down and positive value shifts up.
Let's check the 4 choices.
A.
Since this curve's A is -2, its amplitude is 2 and range is from -2 to 2. BUT since D value is -3, it shifts vertically 3 units down making the range from -1 to -5. Clearly choice A is not true.
B.
This graph is the graph of shifted 3 units DOWN since D is negative. This choice isn't true.
C.
Because of the - (minus) sign in front of the function, the function is reflected about x-axis, but amplitude doesn't change. Since A value is 2, amplitude is 2. This is true.
D.
Period depends on the B value. Here, B value is 1, so period is normal as the parent function of a sine curve, which is , NOT
. So this is not correct.
ANSWER: C is true
Answer:
Congruence between pentagons
Step-by-step explanation:
The relationship occurs because having two congruent Pentagons and generating a segment within them (or outside), congruence is extrapolated to the triangles generated within them. Thus, if there is congruence among the pentagons, it will exist between the formed triangles. In other words since the two pentagons are congruent, the corresponding angle pair is congruent. also the two corresponding side pairs are also congruent.
In the attached image for example, the ABCDE and KLMNO pentagons are congruent, so all of their internal division lines are also congruent (AC and KM)
