Respuesta :
Answer:
P=5 and Q=-3
Step-by-step explanation:
-3+8=p=5
4-7=q=-3
<p, q>= <5,-3>
The composition of the translations; T < − 3 , 4 > ⋅ T < 8 , − 7 > (x, y) as one translation gives;
T < 5 , − 3 > (x, y)
We want to compose the translations; T < − 3 , 4 > ⋅ T < 8 , − 7 > (x, y) as one translation;
Now, translation is usually a map defined as;
T < a , b> < x , y> = (x + a, y + b)
Thus, the image of the first translation is given as;
T < 8 , − 7 > (x, y) = (x + 8, y - 7)
Finally;
T < − 3 , 4 > ⋅ T < 8 , − 7 > (x, y) = T < − 3 , 4 > ⋅ (x + 8, y - 7)
⇒ (x + 8 - 3, y - 7 + 4)
⇒ (x + 5, y - 3)
Since T < a , b> < x , y> = (x + a, y + b)
Then; (a, b) = (5, -3)
As one translation gives;
T < 5 , − 3 > (x, y)
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