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amid [387]
2 years ago
7

) Find the coordinates of the point A' which is the symmetric point

Mathematics
1 answer:
soldier1979 [14.2K]2 years ago
7 0

Let, coordinate of point A' is (x,y).

Since, A' is the symmetric point  A(3, 2) with respect to the line 2x + y - 12 = 0.​

So, slope of line containing A and A' will be perpendicular to the line 2x + y - 12 = 0 and also their center lies in the line too.

Now, their center is given by :

C( \dfrac{x+3}{2}, \dfrac{y+2}{2})

Also, product of slope will be -1 .( Since, they are parallel )

\dfrac{y-2}{x-3} \times -2  = -1\\\\2y - 4 = x - 3\\\\2y - x = 1

x = 2y - 1

So, C( \dfrac{2y -1 +3}{2}, \dfrac{y+2}{2})\\\\C( \dfrac{2y + 2}{2}, \dfrac{y+2}{2})

Also, C satisfy given line :

2\times ( \dfrac{2y + 2}{2})  + \dfrac{y+2}{2} = 12\\\\4y + 4 + y + 2 = 24\\\\5y = 18\\\\y = \dfrac{18}{5}

Also,

x = 2\times \dfrac{18}{5 } - 1\\\\x = \dfrac{31}{5}

Therefore, the symmetric points isA'(\dfrac{31}{5}, \dfrac{18}{5}) .

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Step-by-step explanation:

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uysha [10]

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3 years ago
Which exponential function goes through the points (1,8) and (4,64)?
vova2212 [387]
Plug in (4,64) into each answer choice.

A) 4(2)^x
64 =4(2)^4 
64 = 4(16) 
64 = 64

Answer choice A is correct.

B) f(x) = 2(4)^x
64 = 2(4)^4
64 = 2(256)
64 ≠ 512

Answer choice B is incorrect.

C) f(x) = 4(2)^{-x}
64 = 4(2)^{-4}
64 = 4(-0.0625)
64 ≠ 0.25

Answer choice C is incorrect.

D) f(x) = 2(4)^{-x}
64 = 2(4)^{-4}
64 = 2(0.00390625)
64 ≠ 0.0078125

Answer choice D is incorrect.


Your answer is B<span>) f(x)=2(4)^x</span>
4 0
2 years ago
Estimate 856 + 457 by first rounding each number to the nearest hundred.
Lisa [10]

Answer:

865 = 900

457 = 500

900 + 500 = 1,400

856 + 457 = 1,313

5 0
2 years ago
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Can someone help me with this question?
andre [41]
The y-intercept (where x = 0) of the equation is at -20.

For every 60 the x runs, the y falls by -10. Use rise over run to determine the slope of the equation.

\frac{-10}{60} = - \frac{1}{6}

Slope-intercept form is determined by the following equation:

y = mx + b

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Plug the slope and y-intercept into the equation.

y =  -\frac{1}{6}x - 20
4 0
3 years ago
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