Question

skillstream: reflections of two - dimensional figures with coordinates : 20 coins
triangle abc has vertices at a(3, - 3), b(-2,5), and c(-4,3). triangle abc has vertices at a(-3, - 3), b(2,5), and c(4,3).
which describes the transformation of triangle abc to triangle abc?
translation left 6 units
translation right 4 units
reflection across the x - axis
reflection across the y - axis

Explanation:

Step1: Analyze coordinate - change rule

For a point $(x,y)$ reflected across the $y$-axis, the new point is $(-x,y)$.
For point $A(3, - 3)$ in $\triangle ABC$, after reflection across the $y$-axis, it becomes $A'(-3,-3)$. For point $B(-2,5)$ in $\triangle ABC$, after reflection across the $y$-axis, it becomes $B'(2,5)$. For point $C(-4,3)$ in $\triangle ABC$, after reflection across the $y$-axis, it becomes $C'(4,3)$.

Step2: Check other transformation rules

• Translation left 6 units: If we translate a point $(x,y)$ left 6 units, the new point is $(x - 6,y)$. For $A(3,-3)$, it would be $(3-6,-3)=(-3,-3)$, but for $B(-2,5)$ it would be $(-2 - 6,5)=(-8,5)

eq B'(2,5)$.

• Translation right 4 units: If we translate a point $(x,y)$ right 4 units, the new point is $(x + 4,y)$. For $A(3,-3)$ it would be $(3 + 4,-3)=(7,-3)

eq A'(-3,-3)$.

• Reflection across the $x$-axis: If we reflect a point $(x,y)$ across the $x$-axis, the new point is $(x,-y)$. For $A(3,-3)$ it would be $(3,3)

eq A'(-3,-3)$.

Answer:

Reflection across the $y$-axis