algebra 2a semester online practice
complete this assessment to review what you’ve learned. it will not count toward your grade.
determine if the relations ( r_1 = {(3,7),(0,5),(2,7),(-1,4)} ) and ( r_2 = {(7,3),(5,0),(7,2),(4,1)} ) are inverses.
option #1: no, not all corresponding ordered pairs are reflections of one another across the line ( y = x ).
option #2: yes, all corresponding ordered pairs are reflections of one another across the line ( y = x ).
option #3: yes, all corresponding ordered pairs are reflections of one another across the line ( y = -x ).
(1 point)
option #\square

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Accepted Answer

# Explanation:
## Step1: Recall inverse relation rule
For two relations to be inverses, each ordered pair $(a,b)$ in $R_1$ should have a corresponding $(b,a)$ in $R_2$, and vice - versa (reflection over $y = x$).
## Step2: Check each pair in $R_1$
- For $(3,7)$ in $R_1$, we look for $(7,3)$ in $R_2$. $(7,3)$ is in $R_2$.
- For $(0,5)$ in $R_1$, we look for $(5,0)$ in $R_2$. $(5,0)$ is in $R_2$.
- For $(2,7)$ in $R_1$, we should look for $(7,2)$ in $R_2$. $(7,2)$ is in $R_2$.
- For $(- 1,4)$ in $R_1$, we should look for $(4,-1)$ in $R_2$, but in $R_2$ we have $(4,1)$ instead of $(4, - 1)$.

Since not all corresponding ordered pairs are reflections across $y=x$ (the pair $(-1,4)$ in $R_1$ does not have a corresponding $(4,-1)$ in $R_2$), the relations are not inverses.
# Answer:
Option #1. No, not all corresponding ordered pairs are reflections of one another across the line $y = x$

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Question

Explanation:

Step1: Recall inverse relation rule

Step2: Check each pair in \(R_1\)

Answer: