Question

Quadrilateral QRST will be reflected over the line y = -1-3r"5 4 3 2 14 5--1QR3TSWhat are the coordinates of point T' after this reflection?O (-4,2)(-2,-4)(2, 4)(4, -2)

Answer 1

The coordinate of point T is (2,-4).

The perpendicular distance of point T from the line y=-x can be determined as,

`\begin{gathered} p=\lvert\frac{2-4}{\sqrt[]{(2)^2+(4)^2}}\rvert \\ p=\frac{1}{\sqrt[]{5}} \end{gathered}`

The pependicular distance of point T' can be determined as,

`p^(\prime)=\frac{a+b}{\sqrt[]{a^2+b^2}}`

As, T' is the reflection of T about line y+x=0 hence p=p',

`\frac{a+b}{\sqrt[]{a^2+b^2}}=\frac{1}{\sqrt[]{5}}`

The only coordinate in quadrant IV which satisfies the above equation is (4,-2).

Thus, option (D) is correct.