The three points X(2, -1), Y(8, y) and Z(11, 2) are collinear. Find the value of y.
Answers
Step-by-step explanation:
Given:-
The three points X(2, -1), Y(8, y) and
Z(11, 2) are collinear points
To find :-
Find the value of y?
Solution :-
Given points are X(2, -1), Y(8, y) and
Z(11, 2)
Let (x1, y1) = X(2, -1) => x1 = 2 and y1 = -1
Let (x2, y2) = Y(8, y) = x2 = 8 and y2 = y
Let (x3,6) = Z(11, 2) => x3 = 11 and y3 = 2
Given points are Collinear points.
We know that
If the points (x1, y1) , (x2, y2) and (x2, y3) are collinear points then the area of a triangle formed by the points is equal to zero.
Area of trianagle formed by the points
(x1, y1) , (x2, y2) and (x2, y3) is
∆ = (1/2) | x1(y2-y3)+x2(y3-y1)+x3(y1-y2) | sq.units
On Substituting these values in the above formula then
=> ∆ =(1/2) | 2(y-2)+8(2-(-1))+11(-1-y) | = 0
=> (1/2) | 2(y-2)+8(2+1)+11(-1-y) | = 0
=> (1/2) | 2y-4+8(3)-11-11y | = 0
=> (1/2) | 2y-4+24-11-11y | = 0
=> (1/2) | 9-9y| = 0
=> (1/2)(9-9y) = 0
=> (9-9y) = 0×2
=> 9-9y = 0
=> 9y = 9
=> y = 9/9
=> y = 1
Therefore, y = 1
Answer:-
The value of y for the given problem is 1
Used Concept:-
If the points are collinear points then the area of a triangle formed by the points is equal to zero.
Used formulae:-
Area of trianagle formed by the points
(x1, y1) , (x2, y2) and (x2, y3) is
∆ = (1/2) | x1(y2-y3)+x2(y3-y1)+x3(y1-y2) | sq.units
Points to know:-
The points lie on the same line are Collinear points.
View the attached file.
