Question

The figure shows two triangles on the coordinate grid:

Answer 1

The correct statement is "A translation $5$ units to the right, followed by a $180$-degree counterclockwise rotation about the origin"

$A=(-4,-1), B=(-3,-1), C=(-4,-4)$

$A'=(-1,1), B'=(-2,1), C'=(-1,1)$

Option A:  

$A=(-4,-1)$

Translate $5$ units up, we get $(-4,-1+5)=(-4,4)$.

When rotating a point $270$ degrees counterclockwise about the origin our point $A(x,y)$ becomes $A'(y,-x)$.

So, $270$-degree counterclockwise rotation about the origin will give $(4,4)$.

This is not equal to $(-1,1)$.

So, this option is incorrect.

Option B:  

$A=(-4,-1)$

When rotating a point $270$ degrees counterclockwise about the origin our point $A(x,y)$ becomes $A'(y,-x)$.

So, $270$-degree counterclockwise rotation about the origin will give $(-1,4)$.

Now, translating $5$ units up, we get $(-1,4+5)=(-1,9)$

This is not equal to $(-1,1)$.

So, this option is incorrect.

Option C:  

$A=(-4,-1)$

When rotating a point $180$ degrees counterclockwise about the origin our point $A(x,y)$ becomes $A'(-x,-y).$

So, $180$-degree counterclockwise rotation about the origin will give $(4,1)$.

Now, translating $5$ units right, we get $(4+5,1)=(9,1)$

This is not equal to $(-1,1)$.

So, this option is incorrect.

Option D:  

$A=(-4,-1)$

Translate $5$ units right, we get $(-4+5,-1)=(1,-1).$

When rotating a point $180$ degrees counterclockwise about the origin our point $A(x,y)$ becomes $A'(-x,-y).$

So, $180$-degree counterclockwise rotation about the origin will give $(-1,1)$.

This is equal to $(-1,1)$.

So, this option is correct.

Learn more about translation and rotation here:

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