Question

Find the line of reflection that maps the trapezoid, formed with vertices at `A(-3,1)`, `B(-1,1)`, `C(0,4)` and `D(-4,4)`, onto itself?

Answer 1

`x+2=0`

Explanation:

The trapezoid is formed with its vertices at `A(-3,1)`, `B(-1,1)`, `C(0,4)` and `D(-4,4)`. These have been named to add clarity to answer.

As ordinates of `A` and `B` are same, as also ordinates of `C`and `D`, it the lines `AB` and `CD` are parallel to `x`-axiss and hence it is apparent that `AB`||`CD`.

Further `AD=sqrt((-3-(-4))^2+(1-4)^2)=sqrt10` and
`BC=sqrt((-1-0)^2+(1-4)^2)=sqrt10` and as such `AD=BC` and it is an isosceles trapezium.

Hence the line joining the midpoints of `AB` and `CD` i.e.`(-2,1)` and `(-2,4)` is the line of reflection that maps the trapezoid onto itself, which is parallel to `y`-axis.

and its equation is `x=-2` or `x+2=0`.