Question

.If the point A(0,2) is equidistant from the points B(3,p), C(p,5) ,find p.Also find the length AB​

Answer 1

Answer:

Given,

AB=AC

(AB)

2

=(AC)

2

Distance between two points=

(x

2

−x

1

)

2

+(y

2

−y

1

)

2

(AB)

2

=(AC)

2

⟹(0−3)

2

+(2−p)

2

=(0−p)

2

+(2−5)

2

9+4+p

2

−4p=p

2

+9

p=1

Distance=

(0−3)

2

+(2−1)

2

Distance=

10

Answer 2

Answer:

AB=AC

ABsq=ACsq

(3-0)sq +(p-2)sq=(p-0)sq +(5-2)sq

9+Psq+4-4p=Psq+9

4-4p=0

4p=4

p=1

length of AB= √10units