Question

If a≠b≠0,prove that (a,a²),(b,b²),(0,0) will not be collinear.
(class 10 CBSE SAMPLE PAPER 2017-18 MATHS)

Answer 1

SOLUTION:
Let A(a,a²), B(b,b²), C(0,0) be the coordinates of the given points.

We know that the area of a triangle having vertices (x1,y1), (x2,y2),(x3,y3) is [½(x1(y2-y3)+x2(y3-y1)+x3(y1-y2) Square units.

Area of ∆ABC= [½(x1(y2-y3)+x2(y3-y1)+x3(y1-y2) Square units.

= |½[(a(b²-0)+b(0-a²)+0(a²-b²)]|
= |½(ab²-0+0+a²b+0-0)|
= |½(ab²+a²b)|

≠0  (a≠b≠0) given

Since the area of the triangle formed by the points (a, a²),(b,b²),(0,0) is not zero ,so the given points are not collinear.

HOPE THIS WILL HELP YOU....

Answer 2

Answer:

Step-by-step explanation: