A triangle PQR has initial coordinates of the vertices as P(1,3), Q(4,5), and R(5,3.5). The triangle is rotated in the $X$-$Y$ plane about the vertex P by an angle $ heta$ in the clockwise direction. If $\sin heta = 0.6$ and $\cos heta = 0.8$, the new coordinates of vertex Q are

Question

A triangle PQR has initial coordinates of the vertices as P(1,3), Q(4,5), and R(5,3.5). The triangle is rotated in the $X$-$Y$ plane about the vertex P by an angle $	heta$ in the clockwise direction. If $\sin	heta = 0.6$ and $\cos	heta = 0.8$, the new coordinates of vertex Q are

Accepted Answer

(4.6, 2.8). Take Q relative to P: $(4-1, 5-3) = (3,2)$. For clockwise rotation, the transformed relative coordinates are $(3\cdot0.8 + 2\cdot0.6, -3\cdot0.6 + 2\cdot0.8) = (3.6, -0.2)$. Adding back P gives $(1+3.6, 3-0.2) = (4.6, 2.8)$.

A triangle PQR has initial coordinates of the vertices as P(1,3), Q(4,5), and R(5,3.5). The triangle is rotated in the $X$-$Y$ plane about the vertex P by an angle $\theta$ in the clockwise direction. If $\sin\theta = 0.6$ and $\cos\theta = 0.8$, the new coordinates of vertex Q are

Solution

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