What is the value of "a" if the points (3,5) and (7,1) are equidistant from the point (a,0) - Maths - Coordinate Geometry

Question

What is the value of "a" if the points (3,5) and (7,1) are
equidistant from the point (a,0) ?

Nishima Pasricha · Accepted Answer

Given, P(a, 0) is equidistant from A(3, 5) and
B(7, 1)

∴ AP = PB

⇒ AP2 = PB2

⇒ (5 – 0)2 + (a –
3)2 = (1 – 0)2 + (7 –
a)2 [ Using Distance formula]

⇒ 25 + a 2 – 6a + 9 = 1 +
49 + a2 
– 14a

⇒ 
–16 = 
–8a

⇒ a = 2

Thus, the value of a is 2

What is the value of "a" if the points (3,5) and (7,1) are equidistant from the point (a,0) ?