The points (2,3) and (4,1) are collinear with the point
Share
The points (2,3) and (4,1) are collinear with the point
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Answer:
Step-by-step explanation:
Given :
The points A (2,3) and B(4,1)
To find
The coordinates of a point C(x,y) which is co-linear with A and B
Solution:
If A,B and C are co-linear then
area of ABC =0
⇒
⇒ 2-2y+4y-12+2x=0
⇒ 2x + 2y = 10
⇒ x+y=5
⇒ y=5-x------------------------(1)
We assume that point C is in quadrant I
and x,y are positive integers
then
x=0,1,2,3,4,5
and y=5,4,3,2,1,0
Answer:
Thus the possible coordinates of C are:
(0,5),(1,4),(2,3),(3,2),(4,1) and (5,0)
Formula used:
Area of a triangle
= [(y1 + y2)(x1 – x2 ) + (y1 + y3 )(x3 – x1) – (y2 + y3 ) (x3 – x2 )]