Question:Choose the correct scale factor: A)2 B)1/2 C)3 D)1/3

Mathematics

2 answers:

aleksandrvk [35]3 years ago

7 0

The length of ND = 3 units

The length of N'D' = 6

6 / 3 = 2

The scale factor is 2

Liono4ka [1.6K]3 years ago

4 0

Answer: A) 2

Step-by-step explanation:

The shape has been enlarge which means B and D are ruled out because if a shape gets enlarge its scale factor has to be greater than 1.

We will use the coordinate of the image of D to find the scale factor.

Pre-image: (2,2) Enlarge or image: (4,4)

So as we can see to get from 2 to 4 you will have to multiply by 2. So the scale factor is 2

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Determine the angles made by the vector v = (67)i + (-15)j with the positive x- and y-axes. write the unit vector n in the direc

vivado [14]

Consider the picture attached.

From right triangle trigonometry:

tan(α)=(opposite side)/(adjacent side)=15/67=0.2239

using a scientific calculator we find that arctan(0.2239)=12.62°

thus α=12.62°, is the angle that the vector makes with the positive x-axis.

The angle made with the + y-axis is 12.62°+90°=102.62°.

The length of the vector v can be determined using the Pythagorean theorem:

$|v|= \sqrt{ 67^{2} + 15^{2} }= \sqrt{4489+225}= \sqrt{4714}=68.8$

Thus, to make v a unit vector, without changing its direction, we need to divide v by |v|=68.8.

This means that the x and y components will also be divided by 68.8, by proportionality.

So, the unit vector in the direction of v is:

<span>(67/68.8)i + (-15/68.8)j=0.97 i + (- 0.22)j
</span>

Answer: 12.62°; 102.62°; 0.97 i + (- 0.22)j