Question

Identify the translation rule on a coordinate plane that verifies that triangle A(-5,1), B(-2,7), C(0,1) and triangle A'(-6,0), B'(-3,6), C'(-1,0) are congruent.

Answer 1

Thanks for your question!

The rule is (x-1, y-1). If we plus in the original we will get the translated one very time.

Hope this helps!

Answer 2

Triangle ABC translate 1 unit left and 1 units down to get the triangle A'B'C'. The rule of translation is

`(x,y)\rightarrow (x-1,y-1)`

Explanation:

Given information: In triangle ABC, A(-5,1), B(-2,7), C(0,1). In triangle A'B'C', A'(-6,0), B'(-3,6), C'(-1,0).

Let the rule of translation be

`(x,y)\rightarrow (x-a,y-b)`

where, a is horizontal shift and b is vertical shift.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b<0, then the graph shifts b units up and if b>0, then the graph shifts b units down.

It is given that A(-5,1) and A'(-6,0).

`A(-5,1)\rightarrow A'(-5-a,1-b)`

`A'(-6,0)=A'(-5-a,1-b)`

On comparing both sides, we get

`-6=-5-a\Rightarrow a=1`

`0=1-b\Rightarrow b=1`

The value of a is 1 and value of b is 1. So, the rule of translation is

`(x,y)\rightarrow (x-1,y-1)`

Therefore the triangle ABC translate 1 unit left and 1 units down to get the triangle A'B'C'.