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the coordinates of begin mathsize 16px style increment end stylejrb are j(1, -2) , r(-3, 6) and b(4, 5). what are the coordinates of the vertices of its image after the transformation translation along (2, 1) and a reflection over y = x?

Sagot :

sqdancefan

Answer:

  • J'' = (-1, 3)
  • R'' = (7, -1)
  • B'' = (6, 6)

Step-by-step explanation:

You want the coordinates of points J(1, -2), R(-3, 6), B(4, 5) after translation by (2, 1) and reflection over y = x.

Translation

Translation adds the translation vector each point. Translation by (2, 1) is the transformation ...

  (x, y) ⇒ (x +2, y +1)

Reflection

Reflection over the line y = x causes the coordinates of a point to be swapped:

  (x, y) ⇒ (y, x)

Composition

The composition of the two transformations, translation by (2, 1) and reflection over y=x, results in the transformation ...

  (x, y) ⇒ (y +1, x +2)

That moves the given points to ...

  J(1, -2) ⇒ J''(-1, 3)

  R(-3, 6) ⇒ R''(7, -1)

  B(4, 5) ⇒ B''(6, 6)

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Additional comment

The attachment shows the translated ∆JRB and the same triangle after reflection over the diagonal line y = x. The final position is in red.

View image sqdancefan
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