Question

Arrange the pairs of points in increasing order of slopes of the lines joining them

Answer 1

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

$m=\dfrac{y_2-y_1}{x_2-x_1}$

a) (15,30) and (20,40).

$m_a=\dfrac{40-30}{20-15}=\dfrac{10}{5}=2$

Similarly find the slope of other lines.

b) (12,32) and (18,48).

$m_b=\dfrac{48-32}{18-12}=\dfrac{16}{6}=2.67$

c) (27,12) and (72,32).

$m_c=\dfrac{32-12}{72-27}=\dfrac{20}{45}=0.44$

d) (45,15) and (60,20).

$m_d=\dfrac{20-15}{60-45}=\dfrac{5}{15}=0.33$

e) (27,2) and (243,18).

$m_e=\dfrac{18-2}{243-27}=\dfrac{16}{216}=0.074$

f) (18,63) and (24,84).

$m_f=\dfrac{84-63}{24-18}=\dfrac{21}{6}=3.5$

g) (63,9) and (84,12).

$m_g=\dfrac{12-9}{84-63}=\dfrac{3}{21}=0.143$

After arranging the slopes in increasing order, we get

$m_e$

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)