In the Fig. 5.20, PB is perpendicular segment from the point A (4, 3). If PA = PB then find the coordinates of B.

Formula used:

Let the point P (4, 0)

PB is perpendicular segment from point A to B

∴ let B be (4, –y)

Distance of PA

⇒ PA = √ ((4 – 4)² + (3 – 0)²)

⇒ PA = √ ((0)² + (3)²)

⇒ PA = √ (0 + 9)

⇒ PA= √ 9

⇒ PA = 3

Distance of PB

⇒ PB = √ ((4 – 4)² + (–y – 0)²)

⇒ PB = √ ((4 – 4)² + (–y)²)

⇒ PB = √ ((0)² + (–y)²)

⇒ PB = √ 0 + y²

⇒ PB = y²

i.e. AP = BP

⇒ 3 = √ y²

Squaring both sides

⇒ 9 = y²

⇒ y = √9

⇒ y = 3

∴ Point B is (4, –3)