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amid [387]
3 years ago
7

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

Mathematics
1 answer:
soldier1979 [14.2K]3 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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Binomial -3y^{2}+5xy when added to polynomial 2x^{2} +3y^{2} -5xy+1  gives  polynomial  that does not contain the variable y .

<h3>What is binomial?</h3>

A mathematical expression consisting of two terms connected by a plus sign or minus sign .

Example: x + 2 is a binomial, where x and 2 are two separate terms.

<h3>What is polynomial?</h3>

A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer

According to the question

polynomial 2x^{2} +3y^{2} -5xy+1

when added with  -3y^{2}+5xy  

= 2x^{2}+1   (as 3y^{2} -5xy got cancelled )

that does not contain the variable y

Hence, Binomial -3y^{2}+5xy when added to polynomial 2x^{2} +3y^{2} -5xy+1  gives that does not contain the variable y .

To know more about Binomial and polynomial here :

brainly.com/question/1698358

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Hope this helped

Step-by-step explanation:

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