Following are the calculation to the coordinates of the reflecting image:
Given:
Point: P(3,10)
line: y=1
To find:
reflecting image of line=?
Solution:
Reflection image of a point \((\alpha , \beta)\) about with respect to a line that is \(ax+by+c=0\)
is given by \((h,k)\\\\\)
\(\to \frac{h-\alpha}{a}=\frac{k-\beta}{b}=\frac{-2(a \alpha +b \beta +c)}{a^2+b^2}\\\\\)
therefore
\((\alpha , \beta) =(3,10) \ and\ line\ is\ y-1=0\ that \ is\ a=0,b=1\ and c=-1\\\\\frac{h-3}{0}=\frac{k-10}{1}=\frac{-2(0 +10 -1)}{0^2+1^2}\\\\h-3=k-10=\frac{-2(9)}{1}\\\\h-3=k-10 =-18\\\\k-10 =-18\\\\k=-18+10\\\\k=-8\)
OR
Input interpretation:
\(\text{Reflection} \\\\ \text{point \ \ \ \ \ (3, 10)}\\\\\ \text{mirror \ \ \ \ \ y = 1}\)
Transformed point:
\((3, 10) \to (3, -8)\)
Reflection matrix:
\(\left(\begin{array}{cc}1&0\\0&-1\\\end{array}\right)\)
Transformation:
\((x, y)\to (x, 2 - y)\)
Matrix form of the transformation:
\(\left(\begin{array}{cc}x\\y\\\end{array}\right) \to \left(\begin{array}{cc}0\\2\\\end{array}\right) + \left(\begin{array}{cc}1&0\\0&-1\\\end{array}\right) \left(\begin{array}{cc}x\\y\\\end{array}\right)\)
For visual representation please find the attachment file.
Learn more:
brainly.com/question/19400146
