Use this video to help you answer number 1. Remember these are to help you properly answer the short answer problems on your test!!

Question

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Question 1
Point P is at (-4,5). The point was translated by the rule (x+3,y-6). Then the point was translated again by the rule (x-4,y+2). What quadrant will point P′
be in ?(1 point)
Responses

I
I - no response given

II
II - no response given

III
III - correct

IV
IV - no response given
Question 2
Write the rule for the composition transformation (4 points)
(x -
,y-
​​​​​​​)​​​​​​​
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Answer 1

To solve the question about the final location of point P after the two translations, we'll follow these steps:

1. Identify the original point P:
   Point P is at (-4, 5).

2. Apply the first translation rule (x + 3, y - 6):

   • For the x-coordinate:
     \(-4 + 3 = -1\)
   • For the y-coordinate:
     \(5 - 6 = -1\)
     So after the first translation, the coordinates of point P become \((-1, -1)\).

3. Apply the second translation rule (x - 4, y + 2):

   • For the x-coordinate:
     \(-1 - 4 = -5\)
   • For the y-coordinate:
     \(-1 + 2 = 1\)
     So after the second translation, the coordinates of point P are \((-5, 1)\).

4. Determine the quadrant for point P' (-5, 1):
   The x-coordinate is negative (-5) and the y-coordinate is positive (1). Therefore, point P' is located in Quadrant II.

So for Question 1, the correct response is II.

For Question 2, the composition transformation in terms of (x, y) that combines the previous translations would be:

1. From \((x, y)\) to \((x + 3, y - 6)\)
2. From \((x + 3, y - 6)\) to \((x + 3 - 4, y - 6 + 2) = (x - 1, y - 4)\)

Therefore, the rule for the composition transformation is: \((x - 1, y - 4)\).