Question

Select the similarity transformation(s) that make ABC similar to DEF.

Answer 1

Given:

We get points A(-6,-4), B(-2,-4), C(-6,-1), D(-2,3), E(-2,1) and F(-0.5,3) by observing the given grpah.

Consider the first option for point A(-6,-4).

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

Substitute x=-6 and y=-4, we get

`(-6,-4)\rightarrow(-(-4),-6)`

`(-6,-4)\rightarrow(4,-6)`

There is no point (4,-6) in the DEF triangle.

This is not true.

Consider the second option for point A(-6,-4).

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

Substitute x=-6 and y=-4, we get

`(-6,-4)\rightarrow(-4,6)`

There is no point (-4,6) in the DEF triangle.

This is not true.

Consider the fourth option for point A(-6,-4).

`(x,y)\rightarrow((1)/(2)x,(1)/(2)y)`

Substitute x=-6 and y=-4, we get

`(-6,-4)\rightarrow((1)/(2)(-6),(1)/(2)(-4))`

`(-6,-4)\rightarrow(-3,-2)`

There is no point (-3,-2) in the DEF triangle.

This is not true.

Consider the fifth option for point A(-6,-4).

`(x,y)\rightarrow(x+3,y+2)`

Substitute x=-6 and y=-4, we get

`(-6,-4)\rightarrow(-6+3,-4+2)`

`(-6,-4)\rightarrow(-3,-2)`

There is no point (-3,-2) in the DEF triangle.

This is not true.

Consider the sixth option for point A(-6,-4).

`(x,y)\rightarrow(2x,2y)`

Substitute x=-6 and y=-4, we get

`(-6,-4)\rightarrow(-12,-8)`

There is no point (-12,-8) in the DEF triangle.

This is not true.

Hence there is no similarity between triangle ABC and DEF.