Final answer:
The correct translation rule for moving a point 4 units to the left and 8 units down is t < -4, -8 > (p), which is option c.
option C is correct answer.
Step-by-step explanation:
The question asks to describe the translation of a point that is 4 units to the left and 8 units down using a translation rule. To move a point to the left, we subtract from its x-coordinate, and to move it down, we subtract from its y-coordinate. Therefore, the correct translation rule is t < -4, -8 > (p), which corresponds with option c. This notation means that point p is translated 4 units left and 8 units down.
A translation is a geometric transformation that shifts an object in the coordinate plane without changing its shape or orientation. To describe the translation of a point
�
P that is 4 units to the left and 8 units down, we use translation rules.
Let
�
(
�
,
�
)
P(x,y) be the original coordinates of point
�
P. The translation rule for moving a point
ℎ
h units to the left and
�
k units down is given by
(
�
−
ℎ
,
�
−
�
)
(x−h,y−k).
In this case,
ℎ
=
4
h=4 (4 units to the left) and
�
=
8
k=8 (8 units down). Applying the translation rule to point
�
P, the new coordinates
�
′
P
′
after the translation would be
(
�
−
4
,
�
−
8
)
(x−4,y−8).
So, if the original coordinates of
�
P were
(
�
,
�
)
(x,y), the translated coordinates
�
′
P
′
would be
(
�
−
4
,
�
−
8
)
(x−4,y−8). This means that each x-coordinate is decreased by 4 units, and each y-coordinate is decreased by 8 units, representing the shift to the left and down, respectively.