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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 ___________.
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).
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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