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Answers
Step-by-step explanation:
Given :-
The points A(2,5) ,B(-2,3) and C (5,4)
To find :-
Plot the points on the graph paper and find the area of ∆ABC?
Solution:-
See the above attachment for the graph
Scale :-
On X-axis 1 cm = 1 unit
On Y-axis 1 cm = 1 unit
We get ∆ ABC joining the points after plotting the graph paper.
Finding the Area of ∆ABC:-
Given points are A(2,5) , B(-2,3) , C(5,4)
Let (x1, y1) = (2,5) => x1 = 2 and y1 = 5
Let (x2, y2) = (-2,3) => x2 = -2 and y2 = 3
Let (x3, y3) = (5,4) => x3 = 5 and y3 = 4
We know that
Area of a triangle formed by the points (x1, y1),
(x2, y2) and (x3, y3) is given by
∆ = (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(3-4)+(-2)(4-5)+5(5-3) |
=> ∆ = (1/2) | 2(-1)+(-2)(-1)+5(2) |
=> ∆ = (1/2) | (-2)+(2)+10 |
=> ∆ = (1/2) | -2+2+10 |
=> ∆ = (1/2) | 10 |
=> ∆ = (1/2)×10
=> ∆ = 10/2
=> ∆ = 5 sq.units
Answer:-
Area of the given triangle ABC is 5 sq.units
Used formulae:-
Area of a triangle formed by the points (x1, y1),
(x2, y2) and (x3, y3) is given by
∆ = (1/2) | x1(y2-y3)+x2(y3-y1)+x3(y1-y2) | sq.units
