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Hoochie [10]
2 years ago
9

PLEASE HELP! IM ALMOST DONE WITH THIS ASSIGNMENT PLSSS HELPP ILL GIVE BRAINLIEST SHOW UR WORK

Mathematics
2 answers:
Talja [164]2 years ago
7 0

Answer:

x = -3

y = -8

Step-by-step explanation:

2y = x - 13

3x = y - 1;  let y = 3x + 1

substitute to solve for 'x':

2(3x + 1) = x - 13

6x + 2 = x - 13

5x + 2 = -13

5x = -15

x = -3

solve for 'y':

3(-3) = y - 1

-9 = y - 1

-8 = y

Sergio [31]2 years ago
5 0

Answer:

(-3,-8)

Step-by-step explanation:

<u>Get one of the variables by themself.</u>

3x = y-1

y = 3x+1

<u>Plug that equation into the other one</u>

2(3x+1) = x-13

Distribute the 2 to 3x+1

6x+2 = x-13

Combine like terms

6x+2 = x-13

-x       -x

5x+2 = x-13

    -2        -2

5x = -15

Divide by 5 on both sides

5x = -15

÷5   ÷5

x = -3

Find y

3(-3) = y-1

-9 = y-1

+1       +1

y = -8

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The green triangle is a dilation of the red triangle with a scale factor of s=13 and the center of dilation is at the point (4,2
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Given:

The red figure dilated with a scale factor of s=\dfrac{1}{3} and the center of dilation is at the point (4,2) to get the green figure.

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The coordinates of C' and A.

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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)

In given problem, 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 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).

We assumed that point A is A(m,n).

Using (i), we get

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

From the given figure it is clear that the image of point A is (8,4).

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

On comparing both sides, we get

\dfrac{1}{3}(m-4)+4=8

\dfrac{1}{3}(m-4)=8-4

(m-4)=3(4)

m=12+4

m=16

And,

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

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

(n-2)=3(2)

n=6+2

n=8

Therefore, the coordinates of point A are (16,8).

4 0
3 years ago
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