Question

Prove that the point (3,0) and (4,1) are the vertices of an isosceles right angle triangle.find the area of triangle ?

Answer 1

Vertices of the triangle are A(-3, 0), B(1, -3), C(4, 1)

Distance between two points = (x2 - x1)2+(y2 - y1)2

AB = √[(1 + 3)2 + (-3 -0)2] = 5

BC = √[(4 - 1)2 + (1 + 3)2] = 5

AC = √[(4 + 3)2 + (1 -0)2] = 50 = 52

AB = BC

Therefore, ΔABC is an isosceles triangle.

52 + 52 = (52 )2

⇒ 50 = 50

⇒ (AB)2 + (BC)2 = (AC)2

So, the triangle satisfies the pythagoras theorem and hence it is a right angled triangle.

Area of the isosceles right angled triangle = 1 2 × base × height = 1 2 × 5 × 5 = 12.5 sq units.