Question

The position of the three trees from two cross roads ( perpendicular roads) are respectively (4m,2m) , 7m,5m and 9m,7m. Are these trees in a straight line?

Answer 1

Yes, the trees are in a straight line.

-consider the positions of trees as points on Cartesian X-Y plane, (crossroads are given by X and Y axes)

so we have points a=(4,2) , b=(7,5) , c=(9,7)

These 3 points lie on a straight line if one point lies on line joining the other two points.

-Lets find equation of line joining points a and c

-Equation is given by (y-y1)=slope*(x-x1), where slope=(y2-y1)/(x2-x1)

-Here, a=(x1,y1) and c=(x2,y2)

putting these in our equation, we get equation of line joining point a and c as

y = x - 2

-Since point b=(7,5) satisfies the above derived equation of line, all three points lie on a straight line