# A line segment has endpoints at (0 ,4 ) and (1 , 8 ). If the line segment is rotated about the origin by  pi /2 , translated horizontally by  5 , and reflected about the y-axis, what will the line segment's new endpoints be?

Nov 17, 2017

$\left(- 1 , 0\right) \text{ and } \left(3 , 1\right)$

#### Explanation:

$\text{label the endpoints "A(0.4)" and } B \left(1 , 8\right)$

$\textcolor{b l u e}{\text{First transformation}}$

$\text{under a rotation about the origin of } \frac{\pi}{2}$

• " a point "(x,y)to(-y,x)

$A \left(0 , 4\right) \to A ' \left(- 4 , 0\right) \text{ and } B \left(1 , 8\right) \to B ' \left(- 8 , 1\right)$

$\textcolor{b l u e}{\text{Second transformation}}$

$\text{under a translation } < 5 , 0 >$

• " a point "(x,y)to(x+5,y)

$A ' \left(- 4 , 0\right) \to A ' ' \left(1 , 0\right) \text{ and } B ' \left(- 8 , 1\right) \to B ' ' \left(- 3 , 1\right)$

$\textcolor{b l u e}{\text{Third transformation}}$

$\text{under a reflection in the y-axis}$

• " a point "(x,y)to(-x,y)

$\Rightarrow A ' ' \left(1 , 0\right) \to A ' ' ' \left(- 1 , 0\right)$

$\Rightarrow B ' ' \left(- 3 , 1\right) \to B ' ' ' \left(3 , 1\right)$

$\text{after all 3 transformations}$

$\left(0 , 4\right) \to \left(- 1 , 0\right) \text{ and } \left(1 , 8\right) \to \left(3 , 1\right)$