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atroni [7]
3 years ago
12

Could someone help me arrange these pairs of points in increasing order of the slopes of the lines joining them. (15, 30) and (2

0, 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).
Mathematics
1 answer:
Zina [86]3 years ago
6 0

Answer:

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

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

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

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

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

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

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

Step-by-step explanation:

Required

Arrange in increasing order of slope

Slope (m) is calculated using:

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

So, we have:

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

m = \frac{40 -30}{20- 15}

m = \frac{10}{5}

m =2.00

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

m = \frac{48 -32}{18- 12}

m = \frac{16}{6}

m = 2.67

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

m = \frac{32-12}{72- 27}

m = \frac{20}{45}

m = 0.44

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

m = \frac{20-15}{60- 45}

m = \frac{5}{15}

m = 0.33

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

m = \frac{18-2}{243- 27}

m = \frac{16}{216}

m = 0.07

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

m = \frac{84-63}{24- 18}

m = \frac{21}{6}

m = 3.50

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

m = \frac{12 -9}{84- 63}

m = \frac{3}{21}

m = 0.14

From least to greatest slope, the pair of points are:

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

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

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

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

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

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

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

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