A triangle with the vertices P(3,0),Q(5,1) and R(4,4) is enlarged. If the center of enlargement is (1,0).find the coordinates of the image of the triangle if the scale factor is -2

To find the coordinates of the image of the triangle, we need to apply the formula for enlargement transformation. The formula is:

New coordinates = Center of enlargement + Scale factor * (Original coordinates - Center of enlargement)

Let's apply this formula to each vertex of the triangle.

1. For vertex P(3,0):

New P = (1,0) + -2 * [(3,0) - (1,0)] = (1,0) + -2 * (2,0) = (1,0) + (-4,0) = (-3,0)

2. For vertex Q(5,1):

New Q = (1,0) + -2 * [(5,1) - (1,0)] = (1,0) + -2 * (4,1) = (1,0) + (-8,-2) = (-7,-2)

3. For vertex R(4,4):

New R = (1,0) + -2 * [(4,4) - (1,0)] = (1,0) + -2 * (3,4) = (1,0) + (-6,-8) = (-5,-8)

So, the coordinates of the image of the triangle after enlargement are P'(-3,0), Q'(-7,-2), and R'(-5,-8).