$\bf \textit{middle point of 2 points }\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
X&({{ a}}\quad ,&{{ b}})\quad 
% (c,d)
Y&({{ -8}}\quad ,&{{ 6}})
\end{array}\qquad
% coordinates of midpoint 
\left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right)$

$\bf \left( \cfrac{-8+a}{2}~,~\cfrac{6+b}{2} \right)=\stackrel{M}{(-3,-1)}\implies 
\begin{cases}
\cfrac{-8+a}{2}=-3\\\\
-8+a=-6\\
\boxed{a=2}\\
----------\\
\cfrac{6+b}{2}=-1\\\\
6+b=-2\\
\boxed{b=-8}
\end{cases}$

5 0

3 years ago

A guide wire of length 108 meters runs from the top of an antenna to the ground. If the angle of elevation to the top of the ant

netineya [11]

Answer: Approximately 72.69 meters

Step-by-step explanation:

Antenna height = h

$sin(42.3)=\frac{opposite}{hypotenuse} =\frac{h}{108} \\\\108*sin(42.3)=h\\\\h=72.685$

5 0

2 years ago