Question

using distance formula prove that the following points are collinear (- 5 ,-9),(-5,6),-5,1)

Answer 1

A(-5,-9). B(-5,6) ,C(-5,1)

AB =√(x2-x1)^2+ (y2-y1)^2
= √(-5+5)^2 +(-9-6)^2
=√(-15)^2
=√225
=15 units (1)
BC =√(-5+5)^2 +(6-1)^2
=√(5)^2
=5 units. (2)
AC =√(-5+5)^2+(-9-1)^2
=√(-10)^2
=√100
=10units. (3)


adding (2) and (3)
AC+BC =15 units
AC+BC= AB. {from (1) }

so A(-5,-9) ,B(-5,6) C(-5,1) are collinear


hence prove