Question

A(1, 2) B(2, 3) C(3, 4) are given points. Out of the following which is true ?
AC + BC = AB
AB - BC = AC
C as a midpoint of AB
A B C are not collinear​

Answer 1

Answer:

A (3,4) and B(7,7) and C(x,y) or C'(x,y) are collinear points.

AB = √[(7-3)²+(7-4)²] = 5

AC = 10, given.

Slope of AC = slope of AB = (7-4)/(7-3) = 3/4

=> (y-4)/(x-3) = 3/4 --- (1)

=> 4 y - 3 x = 7 --- (2)

AC² = 10² = (y - 4)² + (x - 3)²

= [ 3/4 * (x - 3) ]² + (x-3)²

= (x-3)² * 25/16

=> x - 3 = + 8

=> x = +11 or -5

=> y = (7+3x)/4

= 10 or -2

C = (11, 10) and C' = (-5, -2)