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VMariaS [17]
3 years ago
8

I will give the Brainliest answer! PLEASE HELP! The vertices of a triangle are located at the points A (1,1) , B (2,3), C (5,0).

The triangle is translated 4 units down, then reflected across the x-axis to obtain triangle A'B'C'. What are the coordinates of the vertices of triangle A'B'C'?
Mathematics
1 answer:
NemiM [27]3 years ago
4 0
1.
The first transformation, the translation 4 units down, can be described with the following symbols:

(x, y) → (x, y-4).

as the points are shifted 4 units vertically, down. Thus the x-coordinates of the points do not change.

A'(1, 1) → A"(1, 1-4)=A"(1, -3).
B'(2, 3) → B"(2, 3-4)=B"(2, -1).
C'(5, 0) → C"(5, 0-4)=C"(5, -4).

2.
The second transformation can be described with:

(x, y) → (x, -y). 

as a reflection with respect to the x-axis maps:

for example, (5, -7) to (5, 7), or (-3, -4) to (-3, 4)


thus, under this transformation A", B", C" are mapped to A', B' and C' as follows:

A"(1, -3)→A'(1, -(-3))=A'(1, 3)
B"(2, -1)→B'(2, -(-1))=B'(2, 1)
C"(5, -4)→C'(5, -(-4))=C'(5, 4)

Answer:

A'(1, 3),  B'(2, 1),   C'(5, 4)

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Answer:

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Step-by-step explanation:

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That means that x = 50 as well, since vertical angles are congruent

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Find the equation for the line that passes through the point (2,2), and that is parallel to the line with the equation y=3/4x-4
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Answer: y=3/4x  + 1/2

Step-by-step explanation: Parallel lines must have the same slope, so you already know the equation must be something like y=3/4x+b. You are given a point that the line goes thru(2,2), so you can plug this point into the equation to solve for b.

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Your team wins 18 medals at a competition. The metals are gold, silver, and bronze in a ratio of 2:4:3. How many of each metal d
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Answer

Find out the how many of each metal did your team win.

To prove

As given

Your team wins 18 medals at a competition.

The metals are gold, silver, and bronze in a ratio of 2:4:3.

Let us assume that x be the scalar multiple of the gold, silver and bronze medal.

Thus

Number of gold medal = 2x

Number of silver medal = 4x

Number of bronze medal = 3x

Than the equation becomes

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x = \frac{18}{9}

x = 2

Number of gold medal = 2 × 2

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3 years ago
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klasskru [66]

Given:

The scale factor is s=\dfrac{1}{3} and the center of dilation is at the point (4,2).

Red is original figure and green is dilated figure.

To find:

The coordinates of point C' and point A.

Solution:

Rule of dilation: If a figure is dilated with a scale factor k and the center of dilation is at the point (a,b), then

(x,y)\to (k(x-a)+a,k(y-b)+b)

According to the given information, the scale factor is \dfrac{1}{3} and the center of dilation is at (4,2).

(x,y)\to (\dfrac{1}{3}(x-4)+4,\dfrac{1}{3}(y-2)+2)            ...(i)

Let us assume the vertices of red triangle are A(m,n), B(10,14) and C(-2,11).

Using (i), we get

C(-2,11)\to C'(\dfrac{1}{3}(-2-4)+4,\dfrac{1}{3}(11-2)+2)

C(-2,11)\to C'(\dfrac{1}{3}(-6)+4,\dfrac{1}{3}(9)+2)

C(-2,11)\to C'(-2+4,3+2)

C(-2,11)\to C'(2,5)

Therefore, the coordinates of Point C' are C'(2,5).

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Using (i), we get

A(m,n)\to A'(\dfrac{1}{3}(m-4)+4,\dfrac{1}{3}(n-2)+2)

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A'(\dfrac{1}{3}(m-4)+4,\dfrac{1}{3}(n-2)+2)=A'(8,4)

On comparing both sides, we get

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\dfrac{1}{3}(n-2)+2=4

\dfrac{1}{3}(n-2)=4-2

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Answer:

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For this, the first thing is to calculate z, which is given by the following equation:

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P (z <1.66) = 0.9515

Which means that the probability that it arrives before 25 minutes is 95.15%

6 0
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