(Q19)Show that the points A(4,2),B(7,5) and C(9,7) are three points lying on a same line.

Answer

Let us find the distances AB,BC,AC by using distance formula

d= √((x2-x1)2 + (y2-y1)2)

So, AB= √(-)2 + (-)2

= √(2 + 2)

= √()

= 3 √() units

BC= √((-)2 + (-)2)

= √(2 + 2)

= √()

= 2 √() units

AC= √((-)2 + (-)2)

= √(2 + 2)

= √

=5 √ units

Now AB+BC=AC therefore that the three points lie on a straight line.