Answer:
(27,2) and (243,18)
(63,9) and (84,12)
(45,15) and (60,20)
(27,12) and (72,32)
(15,30) and (20,40)
(12,32) and (18,48)
(18,63) and (24,84)
Step-by-step explanation:
Formula for slope of a line is
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
a) (15,30) and (20,40).
[tex]m_a=\dfrac{40-30}{20-15}=\dfrac{10}{5}=2[/tex]
Similarly find the slope of other lines.
b) (12,32) and (18,48).
[tex]m_b=\dfrac{48-32}{18-12}=\dfrac{16}{6}=2.67[/tex]
c) (27,12) and (72,32).
[tex]m_c=\dfrac{32-12}{72-27}=\dfrac{20}{45}=0.44[/tex]
d) (45,15) and (60,20).
[tex]m_d=\dfrac{20-15}{60-45}=\dfrac{5}{15}=0.33[/tex]
e) (27,2) and (243,18).
[tex]m_e=\dfrac{18-2}{243-27}=\dfrac{16}{216}=0.074[/tex]
f) (18,63) and (24,84).
[tex]m_f=\dfrac{84-63}{24-18}=\dfrac{21}{6}=3.5[/tex]
g) (63,9) and (84,12).
[tex]m_g=\dfrac{12-9}{84-63}=\dfrac{3}{21}=0.143[/tex]
After arranging the slopes in increasing order, we get
[tex]m_e<m_g<m_d<m_c<a_a<m_b<m_f[/tex]
So, required arrangement of ordered pairs is
(27,2) and (243,18)
(63,9) and (84,12)
(45,15) and (60,20)
(27,12) and (72,32)
(15,30) and (20,40)
(12,32) and (18,48)
(18,63) and (24,84)
