Answer:
So the three new vertices are (0,0) , (-1,-0) , and (-1,3)
Step-by-step explanation:
So let's pick a point on the triangle like (-3,-1).
The center point of dilation is (3,1). The horizontal distance that (3,1) is from (-3,-1) is 3-(-3)=6. The scale factor is 0.5 so multiply 0.5 to the horizontal distance which is 3. The vertical distance that (-3,-1) is from (3,1) is 1-(-1)=2. The scale factor is 0.5 so multiply 2 and 0.5 giving you 1.
So this means the image of the point (-3,-1) is going to be at: starting from center (3,1) move left 3 and down 1 and you are at (0,0).
Or if you prefer just use a formula
(k(x-a)+a,k(y-b)+b)
(x,y) is a point on the triangle
(a,b) is the center=(3,1)
k is the scale factor=.5
So let's do this formula to the other two points...
(x,y)=(-5,-1)
(.5(-5-3)+3,.5(-1-1)+1)
(.5(-8)+3,.5(-2)+1)
(-4+3,-1+1)
(-1,0)
Last point (x,y)=(-5,5)
(.5(-5-3)+3,.5(5-1)+1)
(.5(-8)+3,.5(4)+1)
(-1,3)
So the three new vertices are (0,0) , (-1,-0) , and (-1,3)
