The points A(4, 7), B(p, 3) and C(7, 3) are the vertices of a right triangle, right - angled at B. Find the value of p.

As ABC is a right angled triangle it should verify the Pythagoras theorem.

i.e.

(hypotenuse)² = (base)² + (perpendicular)²

As triangle is right angled at B

Hypotenuse will be AC

So,

(AC)² = (AB)² + (BC)²

By using distance formula i.e.

→ AC =

BC =

AB =

Then, (AC)² = (AB)² + (BC)²

+

→ (7-4)² + (3-7)² = (7- p)² + (3-3)² + (p-4)² + (3-7)²

→ 9 + 16 = p² - 8p + 16 + 16 + 49 + p² - 14p

9 = 2p² - 24p + 65

2p² - 18p + 54 = 0

p² - 12p + 27 = 0

p² - 9p - 3p + 27 = 0

(p - 9)(p - 3) = 0

p = 9 or p = 3