Question

Entrance Ticket on Translations Sarah graphed a triangle with vertices X (3,3) Y (4,1) Z (1,1). She asked her classmate Paul to translate the triangle (x-4) (y+2). Paul stated that the triangle will move down by 4 and right by 2 putting the triangle in the 4th quadrant. Graph the translation to see if Paul is correct? Explain your reasoning. Your explanation should include: • What is a translation? • Is Paul correct? Why or why not • Which direction should you move the triangle? • Which quadrant is the translation located?

Answer 1

The coordinates of the triangle XYZ are:

X(3,3)

Y(4,1)

Z(1,1)

The translation to perform is (x-4) and (y+2)

Translations are rigid transformations of a figure, this means that the triangle will move but won't change its shape or size.

A translation over the x axis results in a horizontal movement.

If you subtract a factor k x-coordinate, the movement will be to the left.

If you add the factor k x-coordinate, the movement will be to the rigth.

In this example the translation over the x-coordinate is (x-4) → 4 unit are being subtracted to the x-coordinate of each point, this results in a horizontal movement 4 units to the left

A translation over the y axis results in a vertical movement.

If you subtract a factor m from the y-coordinate, the movement will be downwards.

If you add the factor m from the y-coordinate, the movement will be upwards

In this example the translation over the y-coordinate is (y+2)→ 2 units were added to the y-coordinate, this results in a vertical movement 2 units up.

Paul moved the triangle 4 units down and 2 units right, he performed the wrong translation.

THe triangle was moved "left" and "up", the translation will be located in the second quadrant