Question

What are the new vertices of triangle ABC, shown, if the triangle is translated two units upward?

Answer 1

To make a vertical translation of a point in the coordinate system you have to add/subtract a "k" number of units to the y-coordinate of the point, leaving the x-coordinate unchanged.

• If you subtract "k" units from the y-coordinate, ,y-k,, the resulting vertical ,movement will be downwards.

,

• If you add "k" units from the y-coordinate, ,y+k,, the resulting vertical ,movement will ve upwards.

In this case, the triangle will be moved two units upwards, which means that you have to add 2 units to the y-coordinates of each vertex, following the rule:

`(x,y)\to(x,y+2)`

First, you have to determine the coordinates of each vertex of the triangle in the coordinate grid:

A(-5,-5)

B(1,1)

C(4,-5)

Next, add 2 units to each y-coordinate to determine the new vertices of ABC

A(-5,-5) → A'(-5,-5+2)=(-5,-3)

B(1,1) → B'(1,1+2)=(1,3)

C(4,-5) → C'(4,-5+2)=(4,-3)

So the new vertices of the triangle after a movement 2 units up are

A'(-5,-3), B'(1,3) and C'(4,-3)

The correct option is B.