Question

Write the equation of the line y = 7x -
4 when dilated by a scale factor of 2
centered at
the point (1,8).​

Answer 1

Given : equation of the line y = 7x - 4  dilated by a scale factor of 2 centered at the point (1,8)  

To Find : Write the equation of the new  line

Solution:

(h , k) is center of dilation

t = scale factor

x'  = (h + t(x - h))

y' = ( k + t(y - k))

Here centered at the point (1,8).

h = 1 , k = 8

t = 2    dilated by a scale factor of 2

=> x'  = ( 1  + 2(x - 1))

=> x' =  2x  - 1

=> x = (x' + 1)/2

=> y'  = ( 8  + 2(y - 8))

=> y' =  2y - 8

=> y = (y' + 8)/2

y = 7x - 4

=>  (y' + 8)/2  = 7 (x' + 1)/2  - 4

=> y' + 8 =  7x' + 7  - 8

=> y' = 7x'  - 16

=> y = 7x - 16

equation of the line y = 7x - 4 when dilated by a scale factor of 2 centered at the point (1,8) will be  y = 7x - 16

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Answer 2

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(h , k) is center of dilation

t = scale factor

x'  = (h + t(x - h))

y' = ( k + t(y - k))

Here centered at the point (1,8).

h = 1 , k = 8

t = 2    dilated by a scale factor of 2

=> x'  = ( 1  + 2(x - 1))

=> x' =  2x  - 1

=> x = (x' + 1)/2

=> y'  = ( 8  + 2(y - 8))

=> y' =  2y - 8

=> y = (y' + 8)/2

y = 7x - 4

=>  (y' + 8)/2  = 7 (x' + 1)/2  - 4

=> y' + 8 =  7x' + 7  - 8

=> y' = 7x'  - 16

=> y = 7x - 16

equation of the line y = 7x - 4 when dilated by a scale factor of 2 centered at the point (1,8) will be  y = 7x - 16