The equation of line u is y=–4x–4. Line u' is the image of line u after a dilation with a scale factor of 14 centered at (5,–8).Which of these points lie on line u'? Select all that apply.(8,0)(1,4)(–2,4)(4,–8)Submit

To find out which points lie on line u', we first need to understand how a dilation with a scale factor of 14 centered at (5, -8) would affect line u.

The equation of line u is y = -4x - 4. A dilation with a scale factor of 14 would multiply both the x and y coordinates of each point on line u by 14, but it would be centered at (5, -8), meaning we would first subtract (5, -8) from each point, then multiply by 14, and then add (5, -8) back.

Let's apply this transformation to each of the given points and see if they still satisfy the equation of line u.

1. (8, 0): After subtracting (5, -8), we get (3, 8). Multiplying by 14 gives (42, 112). Adding (5, -8) back gives (47, 104). Substituting x = 47 into the equation of line u gives y = -4*47 - 4 = -192, which is not equal to 104, so (8, 0) does not lie on line u'.

2. (1, 4): After subtracting (5, -8), we get (-4, 12). Multiplying by 14 gives (-56, 168). Adding (5, -8) back gives (-51, 160). Substituting x = -51 into the equation of line u gives y = -4*-51 - 4 = 200, which is not equal to 160, so (1, 4) does not lie on line u'.

3. (-2, 4): After subtracting (5, -8), we get (-7, 12). Multiplying by 14 gives (-98, 168). Adding (5, -8) back gives (-93, 160). Substituting x = -93 into the equation of line u gives y = -4*-93 - 4 = 368, which is not equal to 160, so (-2, 4) does not lie on line u'.

4. (4, -8): After subtracting (5, -8), we get (-1, 0). Multiplying by 14 gives (-14, 0). Adding (5, -8) back gives (-9, -8). Substituting x = -9 into the equation of line u gives y = -4*-9 - 4 = 32, which is not equal to -8, so (4, -8) does not lie on line u'.

Therefore, none of the given points lie on line u'.