Mathematics: One endpoint of a line segment is at (4, 2). the line is bisected by placing the midpoint of the line segment at (−2, −1). what are the coordinates of the other endpoint? a) (−4, −6) b)(−8, −4) c)(10, 5) d)(−8, 4)

Step-by-step explanation:Right triangle ABC is reflected over AC to form triangle AFC.Triangle AFC dilated by a scale factor of two-thirds to form triangle DEC.Reflection is a rigid transformation which preserves lengths and angles, then Dilation is a transformation which maps the triangle into similar triangle, soThus,Similar triangle have congruent corresponding angles, soand proportional corresponding sidesThus, correct options are:...

One endpoint of a line segment is at (4, 2). the

Ответ:

jon3232

14.03.2022

Mathematics

$\bf ~~~~~~~~~~~~\textit{middle point of 2 points }
\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~ 4 &,& 2~) 
% (c,d)
&&(~ x &,& y~)
\end{array}\qquad
% coordinates of midpoint 
\left(\cfrac{ x_2 + x_1}{2}\quad ,\quad \cfrac{ y_2 + y_1}{2} \right)
\\\\\\
\left( \cfrac{x+4}{2}~~,~~\cfrac{y+2}{2} \right)=\stackrel{midpoint}{(-2~~,~~-1)}\implies 
\begin{cases}
\cfrac{x+4}{2}=-2\\\\
x+4=-4\\
\boxed{x=-8}\\
----------\\
\cfrac{y+2}{2}=-1\\\\
y+2=-2\\
\boxed{y=-4}
\end{cases}$