Question

A point A(-5,-3) is translated by the vector v = <8, 0>, and then reflected about the line y=0. the coordinates of its image A are _________.

Answer 1

(3, 3)

Explanation:

The translation moves the point to the right 8 units. The reflection over the x-axis changes the sign of the y-coordinate.

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translation

A translation vector adds its components to the x- and y-coordinates of the point being translated.

(x, y) ⇒ (x, y) +(8, 0) = (x +8, y) . . . . . translation by <8, 0>

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reflection

The line y=0 is the x-axis. The y-coordinate of a point is the distance of that point from the x-axis. Reflection in the x-axis changes the sign of the y-coordinate, moving the point to an equal distance on the other side of the x-axis.

(x, y) ⇒ (x, -y) . . . . . reflection in the x-axis

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composition of transformations

The net effect of both transformations is ...

(x, y) ⇒ (x +8, -y)

Then the translated and reflected point A will be ...

A(-5, -3) ⇒ A'(-5+8, -(-3)) = A'(3, 3) . . . . coordinates of the image point