Point A is located at (3,-6) and point A is located at (1-2). What is the scale factor?

Mathematics

1 answer:

Anuta_ua [19.1K]3 years ago

4 0

Answer:

The scale factor is 3.

Step-by-step explanation:

Let the origin O(0,0) is the reference point and the coordinates of the point A are given by (3,-6).

Therefore, the distance OA is given by $\sqrt{(3 - 0)^{2} + (- 6 - 0)^{2}} = 3\sqrt{5}$ units.

Again, the coordinates of point A' are (1,-2).

Therefore, the distance OA' is given by $\sqrt{(1 - 0)^{2} + (- 2 - 0)^{2}} = \sqrt{5}$ units.

Hence, the scale factor is $\frac{OA}{OA'} = \frac{3\sqrt{5} }{\sqrt{5}} = 3$ . (Answer)

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Given tan of theta = -2 and pi/2; find cos(2theta)

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Given tan of theta = -2 and pi/2; find cos(2theta)
The identity of cos (2 theta)= $cos(2\theta )=\frac{1-tan^2\theta }{1+tan^2\theta }$
Given tan of theta = -2 and pi/2.
So, let's plug in tan theta= -2
$cos(2\theta)= \frac{1-(-2)^2}{1+(-2)^2}$
= $\frac{1-4}{1+4}$ (Squaring)
= $\frac{-3}{5}$ (simplifying)
So, cos ( 2 theta) = -3/5.
Now we can plug in tan theta = π/2
$cos(2\theta)= \frac{1-(π/2)^2}{1+(π/2)^2}$
= $\frac{1-pi^2/4}{1+pi^2/4}$ (Squaring)
= $\frac{4-pi^2}{4+pi^2}$ Simplifying
So, cos ( 2 theta)= -3/5 and (4-pi^2)/(4+pi^2)