Question

△abc is shown on the coordinate grid.
translation 4 units up and 2 units to the right
translation 4 units down and 2 units to the left
part b
△abc is translated 4 units up and 3 units to the right and is then reflected across the y - axis to create a new △abc. what are the coordinates of the vertices of this new △abc?
a(□,□)
b(□,□)
c(□,□)

Explanation:

Step1: Identify original coordinates

Assume $A(-4,1)$, $B(-3,4)$, $C(-1,0)$.

Step2: Perform translation

For a translation 4 units up and 3 units to the right, the transformation rule for a point $(x,y)$ is $(x + 3,y+4)$.
For point $A$: $(-4 + 3,1 + 4)=(-1,5)$.
For point $B$: $(-3+3,4 + 4)=(0,8)$.
For point $C$: $(-1+3,0 + 4)=(2,4)$.

Step3: Perform reflection across y - axis

The rule for reflecting a point $(x,y)$ across the y - axis is $(-x,y)$.
For the translated point $A'$: $-(-1)=1$, so $A'(1,5)$.
For the translated point $B'$: $-(0)=0$, so $B'(0,8)$.
For the translated point $C'$: $-(2)= - 2$, so $C'(-2,4)$.

Answer:

$A'(1,5)$
$B'(0,8)$
$C'(-2,4)$