Answer: The correct option is (D) P″(9, -12) and Q″(15, -3).
Step-by-step explanation: Given that triangle PQR is dilated by a scale factor of 1.5 to form triangle P′Q′R′. This triangle is then dilated by a scale factor of 2 to form triangle P″Q″R″.
The co-ordinates of vertices P and Q are (3, -4) and (5, -1) respectively.
We are to find the co-ordinates of the vertices P″ and Q″.
<u>Case I :</u> ΔPQR dilated to ΔP'Q'R'
The co-ordinates of P' and Q' are given by

<u>Case II :</u> ΔP'Q'R' dilated to ΔP''Q''R''
The co-ordinates of P'' and Q'' are given by

Thus, the co-ordinates of the vertices P'' and Q'' are (9, -12) and (15, -3).
Option (D) is CORRECT.
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Given the sides of a triangular rug and an included angle between them, the area is calculated through the equation,
A = 0.5ab (cos C)
where a and b are the lengths of the side and C is the included angle.
A = 0.5(5 ft)(4 ft)(cos 79°)
A = 1.9 ft²
Thus, the area of the triangular rug is approximately 1.9 ft².
Answer:
Not enough information
Step-by-step explanation:
one of the catapults could have more force than the other
Answer: d
Step-by-step explanation: just because it is super easy i did this before