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Crazy boy [7]
3 years ago
5

A.) Describe a transformation sequence that will transform quadrilateral ABCD into quadrilateral A’B’C’D’.

Mathematics
1 answer:
Mariulka [41]3 years ago
8 0

a.) The orientation of ABCD is clockwise, as is the orientation of A'B'C'D'. This means the transformation involves a even number of reflections (may be 0). The orientation of AB is North, and the orientation of A'B' is West, so a rotation of 90° CCW (or equivalent) is involved. We can find the point of intersection of the perpendicular bisectors of AA' and BB' (at (-1, -1)) to determine a suitable center of rotation.

ABCD can be transformed to A'B'C'D' by ...

  • rotation 90° CCW about the point (-1, -1)

b.) Rotation by 90° can also be accomplished by reflection across a diagonal line. Since we want the orientation to remain unchanged, we need another reflection to put the figure into its final position. A suitable alternate sequence for mapping ABCD to A'B'C'D' is ...

  • reflection across the line y=x
  • reflection across the line x=-1

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Write the equation of a line in slope-intercept form that passes through the given points.
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Answer:

<h2>         y = 0.25x + 2</h2>

Step-by-step explanation:

\bold{slope\, (m)=\dfrac{change\ in\ Y}{change\ in\ X}=\dfrac{y_2-y_1}{x_2-x_1}}

(0, 2)    ⇒     x₁ = 0,  y₁ = 2

(-4, 1)     ⇒     x₂ = -4,  y₂ = 1

So the slope:

\bold{m=\dfrac{1-2}{-4-0}=\dfrac{-1}{-4}=0.25}

The point-slope form of the equation of the line passing through point (x₀,y₀) and with slope m is:  y - y₀ = m(x - x₀)

m = 0.25

(0, 2)    ⇒     x₀ = 0,  y₀ = 2

Therefore:

               y - 2 = 0.25(x - 0)

               y - 2 = 0.25x                  {add 2 to both sides}

               y = 0.5x + 2          ←  the slope-intercept form of the equation

5 0
3 years ago
The shape of the solution region for the system (picture) can be described as which of the following? Select all that apply.
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3 years ago
How do I find angle a?
vfiekz [6]
The slope of the line is 2/3, so the angle is arctan(2/3) ≈ 33.69°.
8 0
3 years ago
Help ...............
sammy [17]
A straight line is 180° so....

9x+24 +6x - 24 = 180

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On a recent trip to the movies , you see a advertisement for 2 adult tickets and 6 child tickets for $60. Write and equation usi
Igoryamba

Answer:

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Step-by-step explanation:

When asked to write and equation or expression, literally. O verte what is in the question to an algebra. The only difference between expression and equation is that equation shows what goes on the other side of the equals sign when expression doesn’t

Hope this helps

Good Luck

4 0
3 years ago
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