Revision: Algebra >> Reflection Maths (English Medium) ICSE Class 10 CISCE

The two mutually perpendicular number lines intersecting each other at their zeroes are called rectangular axes or coordinate axes, or axes of reference. 

The position of a point in a plane is expressed by a pair of numbers, one concerning the x-axis and the other concerning the y-axis. called co-ordinates. 

• x → distance from y-axis (abscissa)

• y → distance from x-axis (ordinate)

Reflection is a transformation in which the image of a point is formed at the same distance on the opposite side of a line (mirror).

An invariant point is a point whose coordinates do not change after a transformation.

As per the question, we have

AP = BP

`⇒ sqrt((x -5)^2 +(y-1)^2) = sqrt((x+1)^2 +(y-5)^2)`

`⇒(x-5)^2 +(y-1)^2 = (x+1)^2 +(y-5)^2`          (Squaring both sides) 

`⇒x^2 - 10x +25 + y^2 -2y +1 = x^2 +2x +1+y^2 -10y+25`

⇒ –10x – 2y = 2x – 10y

⇒ 8y = 12x

⇒ 3x = 2y

Sign Convention

• Right of y-axis → +x

• Left of y-axis → −x

• Above x-axis → +y

• Below x-axis → −y

Standard Line Results

• x = 0 → y-axis

• y = 0 → x-axis

• x = a → line parallel to the y-axis

• y = b → line parallel to the x-axis

Quadrant Reminder

In x-axis (y = 0)

(x,y) → (x,−y)​

In y-axis (x = 0)

(x, y) → (−x, y)​

In origin

(x, y)→(−x,−y)

Reflection in Parallel Lines:

• In line y = a

  (x, y)→(x, 2a − y)​

• In line x = a

  (x, y)→(2a − x, y)​

• Reflection in the x-axis
   Points on x-axis (x,0)

• Reflection in the y-axis
  Points on y-axis (0,y)

• Reflection in origin
  Only the origin (0,0)

• Reflection in line y = a
  Points lying on the line y = a

• Reflection in line x = a
  Points lying on the line x = a