Question

Drag each tile to the correct boxArrange the pairs of points in increasing order of the slopes of the lines joining them.(15, 30) and (20.40)(12, 32) and (18,48)(27, 12) and (72, 32)(45, 15) and (60, 20)(27, 2) and (243, 18)(18,63) and (24. 84)(63, 9) and (84, 12)2021 Edmentum. All rights reserved.EXTI

Answer 1

We are asked to find the slopes of the given points and arrange them in increasing order.

Recall that the slope is given by

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

Let us first find the slopes of the given points.

1. (15, 30) and (20, 40)

$m_1=\frac{40-30}{20-15}=\frac{10}{5}=2$

2. (12, 32) and (18, 48)

$m_2=\frac{48-32}{18-12}=\frac{16}{6}=\frac{8}{3}=2.67$

3. (27, 12) and (72, 32)

$m_3=\frac{32-12}{72-27}=\frac{20}{45}=\frac{4}{9}=0.44$

4. (45, 15) and (60, 20)

$m_4=\frac{20-15}{60-45}=\frac{5}{15}=\frac{1}{3}=0.33$

5. (27, 2) and (243, 18)

$m_5=\frac{18-2}{243-27}=\frac{16}{216}=\frac{2}{27}=0.07$

6. (18, 63) and (24. 84)

$m_6=\frac{84-63}{24-18}=\frac{21}{6}=\frac{7}{2}=3.5$

7. (63, 9) and (84, 12)

$m_7=\frac{12-9}{84-63}=\frac{3}{21}=\frac{1}{7}=0.14$

Finally, let us arrange the slopes in increasing order (from least to greatest)

$\begin{gathered} m_5=0.07 \\ m_7=0.14 \\ m_4=0.33 \\ m_3=0.44 \\ m_1=2 \\ m_2=2.67 \\ m_6=3.5 \end{gathered}$

Therefore, the increasing order of the slopes is

m5 = 0.07 (27, 2) and (243, 18)

m7 = 0.14 (63, 9) and (84, 12)

m4 = 0.33 (45, 15) and (60, 20)

m3 = 0.44 (27, 12) and (72, 32)

m1 = 2 (15, 30) and (20, 40)

m2 = 2.67 (12, 32) and (18, 48)

m6 = 3.5 (18, 63) and (24. 84)