Question

Triangle ABC is translated 2 units up and 4 units to the right and is then rotated 180° to
produce the image triangle A'B'C'. What are the coordinates of B' in the resulting figure?

Answer 1

Answer:

$B' = (7,-6)$

Step-by-step explanation:

From the attachment, we have that:

$A = (1,8)$

$B = (-3,4)$

$C = (4,-2)$

Required

Determine B'

Taking the translation one at a time:

2 units up

This implies, we add 2 to the y value of the function

$B = (-3,4)$ becomes

$B' = (-3, 4 + 2)$

$B' = (-3, 6)$

4 units right

This implies, we subtract 4 to the x value of the function

$B' = (-3, 6)$ becomes

$B' = (-3 - 4,6)$

$B' = (-7,6)$

180 degrees rotation

Here; B'(x,y) becomes B'(-x,-y)

So, the initial coordinates $B' = (-7,6)$

becomes

$B' = (-(-7),-6)$

$B' = (7,-6)$

Hence:

The final coordinates of B' is $B' = (7,-6)$