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 Question 1 regarding the initial point P at (-4, 5) after two translations, let's break it down step-by-step.

Step 1: First Translation

The first translation rule is (x + 3, y - 6). We will apply this rule to point P.

• Original point P: (-4, 5)
• Applying the translation:
  • x-coordinate: -4 + 3 = -1
  • y-coordinate: 5 - 6 = -1

So, after the first translation, point P' becomes (-1, -1).

Step 2: Second Translation

The second translation rule is (x - 4, y + 2). We will apply this rule to point P' (-1, -1).

• New point P': (-1, -1)
• Applying the translation:
  • x-coordinate: -1 - 4 = -5
  • y-coordinate: -1 + 2 = 1

So, after the second translation, point P'' becomes (-5, 1).

Determining the Quadrant

Now we need to determine the quadrant in which point P'' (-5, 1) lies.

• The x-coordinate is -5 (which is negative).
• The y-coordinate is 1 (which is positive).

In the Cartesian plane, points with a negative x-coordinate and a positive y-coordinate are located in the II Quadrant.

Answer to Question 1:

The correct answer regarding which quadrant point P' will be in is II.

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Question 2: Write the Rule for the Composition Transformation

To write the rule for the composition transformation from the original point P (-4, 5) to point P'' (-5, 1), we can combine both transformation rules.

1. The first transformation: (x + 3, y - 6)
2. The second transformation: (x - 4, y + 2)

To find the overall transformation:

• Starting with (x, y):
  1. Apply the first transformation:
     • New \(x_1 = x + 3\)
     • New \(y_1 = y - 6\)
  2. Apply the second transformation:
     • New \(x_2 = (x + 3) - 4 = x - 1\)
     • New \(y_2 = (y - 6) + 2 = y - 4\)

Thus, the overall rule for the composition transformation is:

(x - 1, y - 4)

Answer to Question 2:

The rule for the composition transformation in the required format is: (x - 1, y - 4)