Question

Perform the following dilation. Dilate around the point (-1,6) with a Scale Factor of 2 After performing this dilation, where will the point J ' be located?

Answer 1

To dilate point J around (-1,6) with a scale factor of 2, find the vector from the center of dilation to J, multiply it by 2, and add the center of dilation's coordinates back to get the dilated point J'.

Step-by-step explanation:

To perform a dilation with a scale factor of 2, around the point (-1,6), each coordinate of point J will be multiplied by the scale factor, and then we adjust for the center of dilation not being at the origin by considering the distance from the center of dilation to point J.

Suppose point J has coordinates (x, y). The dilated point J' will be located at:

• First, subtract the coordinates of the center of dilation from point J to find the vector:
  
  Vector = (x + 1, y - 6)
• Multiply this vector by the scale factor of 2:
  
  Dilated Vector = 2 × (x + 1, y - 6)
• Add the coordinates of the center of dilation to this result to find the coordinates of point J':
  
  J' = (2 × (x + 1) - 1, 2 × (y - 6) + 6)

If J = (x, y), then J' = (2x + 1, 2y - 6).