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maybeemmamay
14.05.2021 •
Mathematics
let P (2,4) be on point on a figure, and let P’ be the corresponding point on the image. the figure is dilated by a scale factor of 4. what is the coordinate of P’?
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Ответ:
Terminal point will be (-
, -
)
Step-by-step explanation:
Terminal point (x, y) on a circle is defined by P(x, y) = ( r cost, r sin t)
Where t is the angle =![\frac{4\pi }{3}](/tpl/images/0502/7133/cdb84.png)
and Radius of the circle = 1 unit [unit circle]
x coordinate = r cost
=![1\times cos\frac{4\pi }{3}](/tpl/images/0502/7133/b73f6.png)
=![cos(\frac{3\pi }{2}-\frac{\pi }{3})](/tpl/images/0502/7133/27d01.png)
= -
[angle lies in third quadrant so the value will be negative]
= -![\frac{1}{2}](/tpl/images/0502/7133/9cdae.png)
y- coordinate = r sint
=![1\times sin\frac{4\pi }{3}](/tpl/images/0502/7133/3eace.png)
= -![sin(\frac{2\pi }{3}-\frac{\pi }{3})](/tpl/images/0502/7133/41e59.png)
= -![(1\times sin\frac{\pi }{3})](/tpl/images/0502/7133/4cb1f.png)
= -![\frac{\sqrt{3} }{2}](/tpl/images/0502/7133/a1d2c.png)
Therefore, terminal point will be (-
, -
)