Question

□ visit www.bigideasmathvideos.com to watch the flipped video instruction for the \try this\try this video for examples 2 & 3 - reflecting in the line $y = x$ and $y = -x$3) graph $overline{ab}$ with endpoints $a(3,-1)$ and $b(3,2)$and its image after a reflection in the line $y = x$.4) graph $overline{ab}$ with endpoints $a(3,-1)$ and $b(3,2)$and its image after a reflection in the line $y = -x$.

Explanation:

Step1: Recall reflection rule for $y=x$

For a point $(x,y)$, reflection over $y=x$ is $(y,x)$.

Step2: Find reflected points for Q3

$A(3,-1) \to A'(-1,3)$; $B(3,2) \to B'(2,3)$

Step3: Recall reflection rule for $y=-x$

For a point $(x,y)$, reflection over $y=-x$ is $(-y,-x)$.

Step4: Find reflected points for Q4

$A(3,-1) \to A'(1,-3)$; $B(3,2) \to B'(-2,-3)$

Step5: Plot original and reflected segments

For Q3: Plot $\overline{AB}$ (vertical line $x=3$, from $(3,-1)$ to $(3,2)$) and $\overline{A'B'}$ (horizontal line $y=3$, from $(-1,3)$ to $(2,3)$).
For Q4: Plot $\overline{AB}$ (same as Q3) and $\overline{A'B'}$ (from $(1,-3)$ to $(-2,-3)$).

Answer:

For Question 3:

• Original segment $\overline{AB}$: connects points $(3, -1)$ and $(3, 2)$
• Reflected segment $\overline{A'B'}$ (over $y=x$): connects points $(-1, 3)$ and $(2, 3)$

For Question 4:

• Original segment $\overline{AB}$: connects points $(3, -1)$ and $(3, 2)$
• Reflected segment $\overline{A'B'}$ (over $y=-x$): connects points $(1, -3)$ and $(-2, -3)$

(When graphing, plot these points and draw straight lines between each pair of corresponding endpoints on the provided grids.)