Rectangleabcd has vertices a(1, 1) , b(1, 7) , c(3, 7) , and d(3, 1) . a dilation with a scale factor of 0.4 and centered at the origin is applied to the rectangle.

which vertex in the dilated image has coordinates of (0.4, 2.8) ?

a′

b′

c′

d′

The correct option is (2) B'.

Step-by-step explanation:  Given that the co-ordinates of the vertices rectangle ABCD are A(1, 1) , B(1, 7) , C(3, 7) , and D(3, 1). A dilation with a scale factor of 0.4 and centered at the origin is applied to the rectangle ABCD.

We are to select the correct vertex of the dilated image that has co-ordinates of (0.4, 2.8).

Let, A'B'C'D' be the dilated image of the rectangle after applying a scale factor of 0.4.

We know,

After dilation, each co-ordinate of every vertex of the original rectangle will be multiplied by the scale factor to give the corresponding co-ordinates of the dilated image.

So, we have

So, the co-ordinates of the vertex B' are (0.4, 2.8).

Thus, option (2) is correct.

statement #3: proof- ang is congruent to ang ecd : angles are congruent.  

step-by-step explanation:

1: the missing angles in statement #3  

a.) acb  

reason- the reason why the answer is acb is because angle ecd and angle acb are both the same size *that's what the word congruent means this is really simple.  

2: the missing word in reason #3  

c.) vertical  

reason- the reason why the answer is vertical is because the angles in that diagram on figure 2 is slanted, which is vertical, and the e and a both lay on vertical lines. along with the other's, but e and a are the 2 main points you want to focus on. and c is kind of like your starting point, because c is for both angles, not just one.  

i hope that was and understanding.

the answer is d.x= 90°

y= 50°

arc lm= 100°

i got this one chief