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If two vertices of a triangle are (1,3) and(4,-1) and the area of triangle is 5sq.units then the angle at the vertex lies in ___________.

If two vertices of a triangle are (1,3) and(4,-1) and the area of triangle is 5sq.units then the angle at the vertex lies in ___________.

Grade:11

2 Answers

Saurabh Koranglekar
askIITians Faculty 10341 Points
one year ago
576-1577_1.PNG
Arun
25763 Points
one year ago

Let the third point on the line y = x + 3 be

(a, a + 3)

Shifting origin to (2, 1), the three vertices are

(0, 0) (a-2, a+2) and (1, - 3)

 

Area, 5 = (1/2) modulus of determinant formed by (a-2, a+2) and (1, - 3)

=> - 3(a - 2) - a - 2 = 10 or - 10

=> - 4a = 6 or - 4a = - 14

=> a = - 1.5 or 3.5

 

=> the third vertex is

(- 1.5, 1.5) or (3.5, 6.5).

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