Question

Using distance formula check weather the points are collinear A(2, 5) B(-1, 2) and C(4, 7)​

Answer 1

Step-by-step explanation:

Given points are, A(2, 5) B(-1, 2) and C(4, 7)

Distance formula : √ ( x2 - x1 )^2 + ( y2 - y1 )^2

AB = √ ( -1 - 2 )^2 + ( 2 - 5 )^2

= √ ( -3 )^2 + ( -3 )^2 = √ 9 + 9 = 3√2

BC = √ [ 4 - (-1 )]^2 + ( 7 - 2 )^2

= √ ( 4 + 1 )^2 + ( 5 )^2 = √ 25 + 25 = 5√2

CA = √ ( 2 - 4 )^2 + ( 5 - 7 )^2

= √ ( -2 )^2 + ( -2 )^2 = √ 4 + 4 = 2√2

from the above, AB + CA = BC

Hence, the given points are collinear