Given the preimage points: find the coordinates of the dilated image using the scale factors. *look at picture*

                                           Question 1)

Please see the explanation.

Step-by-step explanation:

We know that the dilation of an original object shows how much bigger or smaller the image will really get, as compared to the original shape.

Also,

The new coordinates of the image can be determined by multiplying the scale factor with the coordinates of the original object.

Given the preimage points:

The formula of the dilation by a scale factor of 3:

(x, y) → (3x, 3y)

Therefore, the coordinates of the dilated image after the dilation by a scale factor of 3 will be:

A(x, y) → (3x, 3y) = A(0, 5) → (3(0), 3(5)) = A'(0, 15)

B(x, y) → (3x, 3y) = B(4, 9) → (3(4), 3(9)) = B'(12, 27)

C(x, y) → (3x, 3y) = C(-1, -8) → (3(-1), 3(-8)) = C'(-3, -24)

                                               Question 2)

Please see the explanation.

Step-by-step explanation:

Given the preimage points:

The formula of the dilation by a scale factor of 1/2:

(x, y) → (1/2x, 1/2y)

Therefore, the coordinates of the dilated image after the dilation by a scale factor of 1/2 will be:

A(x, y) → (3x, 3y) = A(0, 5) → (1/2(0), 1/2(5)) = A'(0, 5/2)

B(x, y) → (3x, 3y) = B(4, 9) → (1/2(4), 1/2(9)) = B'(2, 9/2)

C(x, y) → (3x, 3y) = C(-1, -8) → (1/2(-1), 1/2(-8)) = C'(-1/2, -4)

an

y = 6x -3y -12

y +3y +12 = 6x

=> . x = { 2y / 3 +2 } this is equation of line in terms of x

=> . if line meets the x-axis the co-ordinates of meeting point would be ( x , 0 )

=> . x = 2 ( 0 ) / 3 + 2

=> . x = 2

so, the point is ( 2 , 0 )