1b. Triangle PQR has vertices P(3, 5), Q(-2, 6) and R(8, -1). Give the coordinates of the vertices after the translation (x, y) → (x + 4, y – 5). What will Q’ (__, __) be?

Question

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(-6, 1)
(2, 10)
(6,1)
(2, 1)

Answer 1

To find the new coordinates of the vertices after the translation \((x, y) \rightarrow (x + 4, y - 5)\), we need to apply the translation to each vertex of triangle PQR.

First, let's translate vertex \( P(3, 5) \):
\[ P' = (3 + 4, 5 - 5) = (7, 0) \]

Next, let's translate vertex \( Q(-2, 6) \):
\[ Q' = (-2 + 4, 6 - 5) = (2, 1) \]

Finally, let's translate vertex \( R(8, -1) \):
\[ R' = (8 + 4, -1 - 5) = (12, -6) \]

So, the coordinates of the vertices after the translation are:
\[ P' = (7, 0) \]
\[ Q' = (2, 1) \]
\[ R' = (12, -6) \]

Thus, the coordinates of \( Q' \) are \( (2, 1) \).