Maths > Straight Lines > 7.0 Reflection of a point about a line
Straight Lines
1.0 Definition
2.0 Condition of collinearity of three points
3.0 Equation of a straight line in various forms
3.1 Point-slope form
3.2 Slope-Intercept form
3.3 Two point form
3.4 Determinant form
3.5 Intercept form
3.6 Normal form
3.7 Parametric form
4.0 Angle between two lines
5.0 Length of perpendicular from a point to a line
6.0 Foot of perpendicular from a point to a line
7.0 Reflection of a point about a line
7.1 Reflection with respect to $X-$axis
7.2 Reflection with respect to $Y-$axis
7.3 Reflection with respect to Origin
7.4 Reflection with respect to the line $x=a$
7.5 Reflection with respect to the line $y=b$
7.6 Reflection with respect to the line $y=x$
8.0 Equation of angle bisector
9.0 Bisector of angle containing origin
10.0 Bisector of angle containing a given point
11.0 Family of straight lines
7.1 Reflection with respect to $X-$axis
3.2 Slope-Intercept form
3.3 Two point form
3.4 Determinant form
3.5 Intercept form
3.6 Normal form
3.7 Parametric form
7.2 Reflection with respect to $Y-$axis
7.3 Reflection with respect to Origin
7.4 Reflection with respect to the line $x=a$
7.5 Reflection with respect to the line $y=b$
7.6 Reflection with respect to the line $y=x$
Let $P(\alpha ,\beta )$ be any point and $Q(x,y)$ be its image about $X-$axis and $M$ is the mid-point of $P$ and
$Q$. Then $$\begin{equation} \begin{aligned} x = \alpha {\text{ and }}y = - \beta \\ Q \equiv (\alpha , - \beta ) \\\end{aligned} \end{equation} $$
which shows that in order to find the reflection with respect to $X-$axis, change the sign of ordinate i.e., $y$-coordinate.
