Answer:
B' (16, 14)
Step-by-step explanation:
Whenever we have a dilation with a scale factor b, we get the new point as:
Let original point be (x,y), then the dilation would make it (bx, by).
There is a diagonal that goes through AC and another through BD. The midpoint of both the diagonal is same. Midpoint formula is:
[tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
Midpoint of AC:
[tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\\=(\frac{2+8}{2},\frac{7+1}{2})\\=(5,4)[/tex]
Now let vertex B have coordinates (x,y). Midpoint of BD:
[tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\\=(\frac{x+2}{2},\frac{y+1}{2})[/tex]
Equate this to the midpoint of AC:
(x+2)/2=5
x+2 = 10
x = 8
and
(y+1)/2=4
y+1=8
y = 7
Thus, B(8,7)
recalling dilation of scale factor 2 rule we said at the beginning, B' would be twice of each coordinate. Hence B' = (16,14)
