5A: Translations

What does a translation do to an image?

• Turns it 90* clockwise

• Mirrors it

• Shrinks it

• Slides it

Answer explanation

Translations are like "transporting" a figure on the coordinate plane. It maintains shape and size. Only position changes.

Translate the blue shape to the green shape...

• 3 Left

  3 Down

• 3 Right

  3 Up

• 2 Right

  3 Up

• 2 Left

  3 Down

Answer explanation

If you follow a particular vertice (corner) of the blue figure, it would need to translate down 3 and left 3 units in order to map to (line up with) with that same vertice (corner) of the green figure.

Translate the blue shape to the green shape...

• 5 Right

  2 Up

• 5 Left

  2 Down

• 5 Right

  5 Up

• 5 Left

  5 Down

Answer explanation

If you follow a particular vertice (corner) of the blue figure, it would need to translate up 2 and right 5 units in order to map to (line up with) with that same vertice (corner) of the green figure.

How is trapezoid ABCD translated to trapezoid A'B'C'D'?

• Translated 5 units down and 5 units to the right

• Translated 5 units down and 1 to the right

• Translated 8 units down and 5 units to the right

• Translated 5 units down and 4 units to the right

Answer explanation

If you follow a particular vertice (corner) of the blue figure, it would need to translate down 8 and right 5 units in order to map to (line up with) with that same vertice (corner) of the green figure.

Determine where T' would be if you translated T 3 units to the right and 6 units up.

• (5, 1)

• (2, -5)

• (-1, 1)

• (8, -2)

Answer explanation

The coordinates of T are (2, -5).

Translating 3 units right means increasing the x value by 3.
Translating 6 units up means increasing the y value by 6.

This means T' will be:

$(2+3,-5+6)\longrightarrow(5,1)$
T' is (5,1)

Where would point J' be if you translated point J 5 units to the left and 2 units up?

• (5, 3)

• (3, -5)

• (-5, 3)

• (-3, 5)

Answer explanation

J is at (0,1)
Translating 5 left means decreasing x by 5.
Translating up 2 means increasing y by 2.

$\left(0-5,\ 1+2\right)\longrightarrow\ \left(-5,3\right)$
J' is at (-5, 3)

How do you represent a translation Algebraically?

• (-y, -x)

• (x + a, y + b)

• (-x , -y)

• (ax, by)

Answer explanation

Translating results in an increase or decrease to the x and/or y values, depending on the translation direction(s) and number of units.

What does this transformation say to do?

(x, y) -----> (x, y +4)

• Translate down 4

• Translate up 4

• Translate right 4

• Translate left 4

Answer explanation

(x, y) -----> (x, y +4)

If the y-value increases by 4, this will be higher (up) on the graph. As a result, the point/figure will translate up by 4.

What transformation is happening?

(x, y) ----> (x + 2, y - 3)

• Translate up 2, left 3

• Translate right 2, up 3

• Translate right 2, down 3

• Translate left 3, right 2

Answer explanation

(x, y) ----> (x + 2, y - 3)

If the x-value increases by 2, this will be further right on the graph. As a result, the point/figure will translate right by 2.

If the y-value decreases by 3, this will be lower (down) on the graph. As a result, the point/figure will translate down by 3.

What coordinate notation rule describes the translation? (From pre-image to image)

• (x - 6, y + 2)

• (x - 2, y + 6)

• (x + 2, y - 6)

• (x + 6, y - 2)

Answer explanation

If you follow a particular vertice (corner) of the blue figure, it would need to translate down 6 and right 2 units in order to map to (line up with) with that same vertice (corner) of the green figure.

Translating down 6 decreases the y-value.
Translating right 2 increases the x-value.

For example:
T (-2, 2) -> T' (0, -5)

The rule:

$(x,y)\longrightarrow(x+2,y-6)$