Question

1. select all of the coordinate pairs that could be part of a proportional relationship with a constant of proportionality of 4. a. (3,12) b. (4,8) c. (3.5,14) d. (6,10) e. (\frac{1}{2},2) 11. here is triangle def and its dimensions. which measurements represent the dimensions of a triangle that is a scaled copy of triangle def? a. 20 cm, 12 cm, 24 cm b. 9 cm, 5 cm, 10 cm c. 27 cm, 16 cm, 33 cm d. 13.5 cm, 7.5 cm, 16.5 cm

Explanation:

Question 10

Step1: Recall the formula for proportional relationship

For a proportional relationship \(y = kx\), where \(k\) is the constant of proportionality. Here \(k = 4\), so \(y=4x\).

Step2: Check each coordinate pair

• For pair A \((3,12)\):

Substitute \(x = 3\) into \(y = 4x\). Then \(y=4\times3=12\).

• For pair B \((4,8)\):

Substitute \(x = 4\) into \(y = 4x\). Then \(y=4\times4 = 16
eq8\).

• For pair C \((3.5,14)\):

Substitute \(x = 3.5\) into \(y = 4x\). Then \(y=4\times3.5=14\).

• For pair D \((6,10)\):

Substitute \(x = 6\) into \(y = 4x\). Then \(y=4\times6=24
eq10\).

• For pair E \((\frac{1}{2},2)\):

Substitute \(x=\frac{1}{2}\) into \(y = 4x\). Then \(y=4\times\frac{1}{2}=2\).

Step1: Find the scale factor

Let the sides of \(\triangle DEF\) be \(a = 18\space\text{cm}\), \(b = 10\space\text{cm}\), \(c=22\space\text{cm}\)

• For option A:

Check the ratios \(\frac{20}{10}=2\), \(\frac{12}{18}=\frac{2}{3}\), \(\frac{24}{22}=\frac{12}{11}\). Ratios are not equal.

• For option B:

Check the ratios \(\frac{9}{18}=\frac{1}{2}\), \(\frac{5}{10}=\frac{1}{2}\), \(\frac{10}{22}=\frac{5}{11}\). Ratios are not equal.

• For option C:

Check the ratios \(\frac{27}{18}=\frac{3}{2}\), \(\frac{16}{10}=\frac{8}{5}\), \(\frac{33}{22}=\frac{3}{2}\). Ratios are not equal.

• For option D:

Check the ratios \(\frac{13.5}{18}=\frac{3}{4}\), \(\frac{7.5}{10}=\frac{3}{4}\), \(\frac{16.5}{22}=\frac{3}{4}\). Ratios are equal.

Answer:

A. \((3,12)\), C. \((3.5,14)\), E. \((\frac{1}{2},2)\)

Question 11