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QuestionFind the translation from point Q(−9,−5)Q(-9,-5) to Q′(−2,−8)Q^{\prime}(-2,-8) as ⟨x,y⟩\langle x, y \rangle.

Studdy Solution

STEP 1

Assumptions1. We are given two points in a space, Q and Q'. . Q is at the position (-9, -5).
3. Q' is at the position (-, -8).
4. The translation that maps Q to Q' is a vector that we need to find.

STEP 2

The translation vector is found by subtracting the coordinates of the initial point (Q) from the coordinates of the final point (Q'). This can be written as⟨x,y⟩=(xQ′,yQ′)−(xQ,yQ)\langle x, y \rangle = (x_{Q'}, y_{Q'}) - (x_{Q}, y_{Q})

STEP 3

Now, plug in the given values for the coordinates of Q and Q' to calculate the translation vector.
⟨x,y⟩=(−2,−8)−(−9,−5)\langle x, y \rangle = (-2, -8) - (-9, -5)

STEP 4

Perform the subtraction operation for each component of the vector separately.
⟨x,y⟩=(−2−(−9),−8−(−))\langle x, y \rangle = (-2 - (-9), -8 - (-))

STEP 5

implify the subtraction operation.
⟨x,y⟩=(7,−3)\langle x, y \rangle = (7, -3)The translation that maps Q to Q' is ⟨7,−3⟩\langle7, -3 \rangle.

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