Question

If the point A(0,2) is equidistant from the points B (3 , P ) and C ( 4 , 5 ) Find thIf the point A(0,2) is equidistant from the points B (3 , P ) and C ( 4 , 5 ) Find the value of P . Also find the length of AB. Also find the length of AB

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

The values of P are 6 and -2.

 Length of AB =5 cm  

Step-by-step explanation:

Given that the point A(0,2) is equidistant from the points B(3,P) and C(4 ,5)

we have to find the value of P and length of AB

Distance of AB=Distance of AC    (∵ Given)

⇒ $\sqrt{(3-0)^2+(P-2)^2}=\sqrt{(4-0)^2+(5-2)^2}\\\\9+P^2+4-4P=16+9\\\\P^2-4P+13=25\\\\P^2-6P+2P-12=0\\\\P(P-6)+2(P-6)=0\\\\(P-6)(P+2)=0$

P=6, -2

Now, as length of AC is

$\sqrt{(4-0)^2+(5-2)^2}$

$=\sqrt{16+9}=5 cm$

⇒  Length of AB =5 cm    (∵ given equal)