Question

. Find the value of p if the points A(2, 3), B(4, p), C( 6, -3) are collinear​

Answer 1

Step-by-step explanation:

A(2,3) B(4,p) C(6,-3)

by using distance formula

AB=√(4-2)²+(p-3)²

CB=√(6-4)²+(-3-p)²

now,

if we write, AB=CB thn

√(4-2)²+(p-3)²=√(6-4)²+(-3-p)²

by squaring on both side ( this done to remove the square roots

hence,

(4-2)²+(p-3)² = (6-4)²+(-3-p)²

(2)²+ p²+3²-6p = (2)²+(-3)²+p²+6p}

here I have used the formula , (a-b)²=a²+b²-2ab.

now,

4+p²+9-6p = 4+9+p²+6p

13+p²-6p = 13+p²+6p

here 13 and p² will be cancelled because when we bring 13 from user right hand side to left hand side it will get negative, for example,

13-13+p²-p²-6p-6p=0

here 13-13 =0 and p²-p² will also get cancelled

hence,

-6p-6p=0

-12p=0

p=12

therefore, p=12 is the answer