The points A (4, 7), B (p, 3) and C (7, 3) are the vertices a right triangle, right-angled at B find the value of p.
Given ,
The vertices of a right triangle, such as,
A (4, 7), B (p, 3) and C (7, 3) 
In right ΔABC, using Pythagoras theorem
(AB)2 + (BC)2 = (AC)2
⇒ [(3 - 7)2 + (p - 4)2] + [(3-3)2 +(7 - p)2] = [(3-7)2 + (7 - 4)2]
⇒ (p - 4)2 + (7 - p)2 = 9
⇒ p2 + 16 -8p + 49 + p2 - 14p = 9
⇒ 2p2 - 22p + 56 = 0
⇒ p2 - 11p + 28 = 0
⇒ p2 - 4p -7p + 28 =0
⇒ p(p - 4) -7(p - 4)=0
⇒ (p - 7 )(p - 4) = 0
⇒ p - 7 = 0 or p - 4 = 0
⇒ p = 7 or p = 4
Hence, the value of p is 4 or 7
