SOLUTION: Show that (1,2), (4,6) and (10,14) are collinear By using the distance formula. And slope!

Question 563408: Show that (1,2), (4,6) and (10,14) are collinear By using the distance formula.
And slope!
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Distance between two points (1,2)(4,6)
x1 y1 x2 y2
d=
1 2 4 6
d=
d=
d=
d=5
Distance between two points (10,14)(4,6)

x1 y1 x2 y2
d=
10 14 4 6
d=
d=
d=
d= 10.00

Distance between two points (10,14) (1,2)
x1 y1 x2 y2
d=
10 14 1 2
d=
d=
d=
d= 15.00
5+10 = 15
A=(4,6), B=(10,14) C=(1,2)
d(BC) = 15
d(AB)=10
d(AC)=5
d(AB) +d(AC)= d(BC)
10+5=15
This is possible only if the points are colinear, else the sum of any two distances will not be equal to the third distance.

so the points are colinear.
BY slopes (1,2)(4,6)
x1 y1 x2 y2
1 2 4 6

slope m =(y2-y1)/(x2-x1)
(6-2)/( 4-1)
( 4 / 3 )
m= 4/ 3

(4,6)(10,14)
x1 y1 x2 y2
4 6 10 14

slope m = (y2-y1)/(x2-x1)
(14-6)/(10-4)
(8/6)
m= 4/ 3
the slopes are same

RELATED QUESTIONS
show that the pionts A(1,-1), B(4,-2) and C(16,1) are... (answered by MathLover1)

The coordinates of points A, B, and C are A(-4, 6), B(-1, 2), and C(2,-2). (a) Show... (answered by math_tutor2020,mccravyedwin,ikleyn,Edwin McCravy)

find the distance bewteen the points using the distance formula: 1) (6,4) , (-8,11) (answered by ewatrrr)

Okay I have to graph the points A(-5,0) , B(3, 2) C(5, 6) and D(-3 4). Then show that... (answered by rothauserc)

A(2;3),b(-2;-1) and c(-3;-2).show that these points are... (answered by Timnewman)

Show that A(2,3) B(-2,-1) and C(-3,-2) are collinear... (answered by josgarithmetic,MathTherapy)

If P=(-2,0) Q=(10,-14) and R=(-4, -2), is PQ=QR, using the distance... (answered by Alan3354)

Determine whether the three points P(-6, -9, 4), Q(-8, -13, -2) and R(-10, -17, -10) are... (answered by KMST)

True or false: the points (4,2) (8,10) and (11,16) are... (answered by mananth,math_tutor2020,greenestamps)