Question

Abc is reflected across the y-axis and then dilated by a factor of 3 using the point (-1,2) as the center of dilation. What is the transformation of B(5,3)?

Answer 1

The correct option is D.

Explanation:

The coordinates of point B are (5,3).

If ABC is reflected across the y-axis, then

`(x,y)\rightarrow (-x,y)`

The coordinates of point B after reflection are

`B(5,3)\rightarrow B_1(-5,3)`

Then dilated by a factor of 3 using the point (-1,2) as the center of dilation.

`(x,y)\rightarrow (3(x+1)-1,3(y-2)+2)`

The coordinates of point B after reflection and dilation are

`B_1(-5,3)\rightarrow B'(3(-5+1)-1,3(3-2)+2)`

`B_1(-5,3)\rightarrow B'(3(-4)-1,3(1)+2)`

`B_1(-5,3)\rightarrow B'(-13,5)`

The transformation of B(5,3) is B'(-13,5). Therefore the correct option is D.

Answer 2

Option D. B''(-13,5)

Explanation:

B=(5,3)=(xb,yb)→xb=5, yb=3

P=(-1,2)=(x,y)→x=-1, y=2

Factor of dilation: f=3

If the point B=(5,3) is reflected across the y-axis, the image is the point:

B'=(-xb,yb)→B'=(-5,3)=(xb',yb')→xb'=-5, yb'=3

Now, if the point B'=(-5,3) is dilated by a factor of 3 using the point P=(-1,2) as the center of dilation, the image is the point:

B''=(x+f(xb'-x),y+f(yb'-y))=(-1+3(-5-(-1)),2+3(3-2))=(-1+3(-5+1),2+3(1))=(-1+3(-4),2+3)

B''=(-1-12,5)→B''=(-13,5)