USING the Midpoint Formula , POINT A is at (-3,-5) and point M is at (-0.5,0). what are the coordinates of point B

1 answer:

7 0

$\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{-3}~,~\stackrel{y_1}{-5})\qquad B(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{x-3}{2}~~,~~\cfrac{y-5}{2} \right)~~=~~\stackrel{\stackrel{Midpoint}{M}}{(-0.5~,~0)}\implies \begin{cases} \cfrac{x-3}{2}=-0.5\\[1em] x-3=-1\\ \boxed{x= 2}\\ \cline{1-1} \cfrac{y-5}{2}=0\\[1em] y-5=0\\ \boxed{y=5} \end{cases}$

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Hey can you please help me posted picture of question :)

sergejj [24]

Answer:
The solutions are:
x = -5
x = -6

Explanation:
To get the solution, we can either use a graphical method or an algebraic method.

1- graphical method:
The solution of the equation would be the values of the x-intercept.
Graphing the equation (check attached image), we would find that the solutions are: -6 and -5

2- algebraic method:
The general formula of the quadratic equation is:
ax² + bx + c = 0
The given equation is:
x² + 11x + 30 = 0
By comparison:
a = 1
b = 11
c = 30
To get the roots, we will substitute in the quadratic formula (attached in the images)
Doing this, we will find that:
either x = $\frac{-11 + \sqrt{(11)^2-4(1)(20)} }{2(1)}$ = -5

or x = $\frac{-11 - \sqrt{(11)^2-4(1)(20)} }{2(1)}$ = -6

Hope this helps :)

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Colt1911 [192]

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