Which statement accurately explains whether a reflection over the X-axis and a 180° rotation would map figure ACB onto itself?
2 answers:
Using transformation rules, it is found that the correct option is:
No, A'C'B' is located at A(-1,1), C'(-3,4) and B'(-5,1).
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- The transformation rule for a reflection over the x-axis is
- The transformation rule for a rotation of 180º is
- After the reflection over the x-axis:
- Taking the reflection, and rotating:
.
- Not the same rule, that is,
, so it would not map figure onto itself.
- A(1,1) would be mapped to A(-1,1), for example, thus, the correct option is:
No, A'C'B' is located at A(-1,1), C'(-3,4) and B'(-5,1).
A similar problem is given at brainly.com/question/10547006
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<h2>Explanation:</h2><h3>Part A.</h3>
The boundary lines of both inequalities will be dashed, because neither includes the "or equal to" case.
The first inequality solution area is bounded by a line with slope +5 and y-intercept +5. The solution area is above the line (y is greater than ...). Since the line rises steeply, the solution area looks to be to the left of the line. (It is shaded red on the attached graph.)
The second inequality solution area is bounded by a line with slope -1/2 and y-intercept +1. The solution area for this inequality is also above the line.
The solution area is where the two solution spaces overlap, in the quadrant to the upper left of the point where the lines intersect.
___
<h3>Part B.</h3>The graph shows the point (-2, 5) to be in the solution space.
We can show this point satisfies both inequalities.
- 5 > 5(-2)+5 ⇒ 5 > -5 . . . true
- 5 > (-1/2)(-2) +1 ⇒ 5 > 2 . . . true