Question

Point P is reflected across two lines. Point E is its reflection image. Which two lines is point P reflected across?

Answer 1

The point P reflected across the lines x=3 and y=2.

Explanation:

From the given graph it is clear that the coordinates of P are (0,0) and the coordinates of E are (6,4).

`P(0,0)\rightarrow E(6,4)` .... (1)

If the origin reflected across the line x=a then

`(0,0)\rightarrow (2a,0)`

If the origin reflected across the line y=b, then

`(0,0)\rightarrow (0,2b)`

If the origin reflected across the line x=a and y=b, then

`(0,0)\rightarrow (2a,2b)` .... (2)

From (1) and (2) we get

`2a=6\Rightarrow a=3`

`2b=4\Rightarrow b=2`

The value of a is 3 and the value of b is 2. Therefore the point P reflected across the lines x=3 and y=2.

Answer 2

Line DJ: x=3. The reflection of point P across Line DJ is the point (6,0)
Line y=2. The reflection of point (6,0) acroos line y=2 is the point E=(6,4)

Answer: The point P is reflected across lines x=3 and y=2