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astraxan [27]
3 years ago
10

Identify the reflection rule on a coordinate plane that verifies that triangle A(-2,3), B(-3,-2), C(-10,0) and triangle A'(2,3),

B'(3,-2), C'(10,0) are congruent when reflected over the y-axis.
A) (x, y) → (-x, -y)

B) (x, y) → (x, -y)

C) (x, y) → (-x, y)

D) the triangles are not congruent

Pleeease answer I need this asap! 15 points!
Mathematics
1 answer:
stich3 [128]3 years ago
4 0

Answer:

D

Step-by-step explanation:

These triangles would be Slided or Translated across a coordinate plane not reflected. :)

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Step 1: Factor 2 x^{2} - 3x -2
1. <span> Multiply 2 by -2, which is -4.</span>
2. <span>Ask: Which two numbers add up to -3 and multiply to -4?
</span>3. <span>Answer: 1 and -4
</span>4. Rewrite -3x as the sum of x and -4x

2 x^{2} +x-4x-2\ \textless \ 0


Step 2: <span>Factor out common terms in the first two terms, then in the last two terms.

</span>x(2x+1)-2(2x+1)\ \textless \ 0
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Step 3: </span>Factor out the common term 2x+1

(2x+1)(x-2)\ \textless \ 0

Step 4: Solve for x

1. Ask: When will (2x+1)(x-2) equal zero?
2. Answer: When 2x + 1 = 0 or x-2=0
3. <span>Solve each of the 2 equations above:

</span>x=- \frac{1}{2} ,2
<span>
Step 5: </span>From the values of x <span>above, we have these 3 intervals to test.
x = < -1/2
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x > 2

Step 6: P</span><span>ick a test point for each interval

</span>For the interval x\ \textless \ - \frac{1}{2} &#10;
Lets pick x=-1. Then, 2(-1) ^{2} -3 * -1 -2 \ \textless \  0
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Drop this interval.
<span>
For this interval - \frac{1}{2} \ \textless \ x\ \textless \ 2
Lets pick x=0. Then, 2* 0^{2} - 3 * 0-2\ \textless \ 0. After simplifying, we get -2\ \textless \ 0, which is true. Keep this <span>interval.

For the interval </span>x\ \textgreater \ 2

Lets pick x = 3. Then, 2 * 3  ^{2} -3*3-2\ \textless \ 0. After simplifying, we get 7\ \textless \ 0, Which is false. Drop this interval.

.Step 7: Therefore, 
- \frac{1}{2} \ \textless \ x\ \textless \ 2

Done! :)</span>
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3 years ago
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