If a `nebne0,` prove that the points `(a,a^(2)),(b,b^(2)),(0,00)` will – InterviewSolution

InterviewSolution

1.	If a `nebne0,` prove that the points `(a,a^(2)),(b,b^(2)),(0,00)` will not be colliear.
Answer» Let the 3 points A `-=(a,a^(2)),B-=(b,b^(2))and C-=(0,0)` from a triangle ABC. `therefore` Area of `DeltaABC=1/2\|a(b^(2)-0)+b(0-a^(2))+0(a^(2)-b^(2))\|` `=1/2[ab^(2)-a^(2)b]=1/2ab(b-a)ne0" "(becauseanebne0)` So, `DeltaABC` will be formed. Therefore 3 points A, B and C will not be collinear.

Discussion

No Comment Found

Related InterviewSolutions

Student of a school are standing in rows and columns in their playground for a drill practice. A, B, C, D are the positions of four students as shown in the figure. Is it possible to place Jaspal in the drill in such a way that he is equidistant from eachl of the four students A, B, C and D? If so, what should be his position ?
Wrtie the slope of X-axis and Y-axis .
Seg AB is parallel to Y-axis and Co-ordinates of point A are `(1,3)` then co-ordinates of point B can be ………….. A)`(3,1)` B)`(5,3)` C)`(3,0)` D)`(1,-3)`A. `(3,1)`B. `(5,3)`C. `(3,0)`D. `(1,-3)`
Out of the following, Point _________ lies to the right of the origin on X- axis.A. `(-2,0)`B. `(0,2)`C. `(2,3)`D. `(2,0)`
The points A(4, 7), B(p, 3) and C(7, 3) are the vertices of a right triangle, right-angled at B. Find the value of p.
Prove that the points (5, -2), (-4, 3) and (10, 7) are the vertices of an isosceles right-angled triangle.
Find the area of the triangle, whose vertices are (a,c+a), (a,c) and (-a,c-a).
Find the area of triangle, whose vertices are (2,3), (7,5) and (-7,-5).
Find the co-ordinates of a point which divides the line joining the points `A(5, -2) and B(4, 6)` in the ratio 1 : 2 externally.
If (x,y) be any point on the line segment joinijng the points (a,0)and (0,b) then prove that `x/b+y/b=1.`