Question

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

Answer 1

(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)

Explanation:

Formula for slope of a line is

`m=(y_2-y_1)/(x_2-x_1)`

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

`m_a=(40-30)/(20-15)=(10)/(5)=2`

Similarly find the slope of other lines.

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

`m_b=(48-32)/(18-12)=(16)/(6)=2.67`

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

`m_c=(32-12)/(72-27)=(20)/(45)=0.44`

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

`m_d=(20-15)/(60-45)=(5)/(15)=0.33`

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

`m_e=(18-2)/(243-27)=(16)/(216)=0.074`

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

`m_f=(84-63)/(24-18)=(21)/(6)=3.5`

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

`m_g=(12-9)/(84-63)=(3)/(21)=0.143`

After arranging the slopes in increasing order, we get

`m_e<m_g<m_d<m_c<a_a<m_b<m_f`

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)