Question

4. Show that the point P (7,3) is equidistant from the points A (20,3);
B (19, 8) and C (2, -9).
TY
f 10 units from the point​

Answer 1

Answer:

Let variable cut coordinate axes at A(a,0,0),B(0,b,0),C(0,0,c)

Then equation of the plane will be

a

x

=

b

y

=

c

z

=1

Let P(α,β,γ) be centroid of tetrahedron OABC.

Then, α=

4

a

,β=

4

b

,γ=

4

c

Volume of tetrahedron =

3

1

(area of △AOB).OC

⇒64k

3

=

3

1

(

2

1

ab)c=

6

abc

⇒64k

3

=

6

(4α)(4β)(4γ)

⇒

64

64×6k

3

=αβγ

Required locus of P(α,β,γ) is xyz=6k

3

solution