Question

If the points (x, y), (2, 3) & (−3, 4) are collinear then (a) x + y = 17 (b) x − y = 17 (c) x − 5y = 17 (d) x + 5y = 17

Answer 1

Answer:

ANSWER

Given A,B,C are collinear and AB=BC

So, B is the midpoint of the line segment AC.

by using midpoint formula

x=(

2

x

1

+x

2

)andy=(

2

y

1

+y

2

)

So

2

5+x

=3

5+x=6

x=1

Also,

2

2+y

=4

2+y=8

y=6

Hence, C(x,y) is C(1,6)

Answer 2

Answer:

equation of line joining (2,3),(-3,4) is

y-3=(4-3)/(-3-2)×(x-2)

y-3=1/5×(2-x)

5y-15=2-x

x+5y-17=0

since (x,y) and other points are collinear, (x,y) is the point on the line

x+5y=17

SO OPTION D IS CORRECT