Find the area of the triangle whose vertices are (1,2), (3,7) and (5,3).

Given: Vertices of a triangle as (1,2), (3,7) and (5,3).

To find Area of a triangle.

Using the formula to find the area of the triangle when vertices (x₁, y₁), (x₂, y₂), (x₃, y₃) are given:

Area of triangle = 1/2|[x₁(y₂ – y₃) + x₂(y₃ - y₁) + x₃(y₁ – y₂)]|

= 1/2 |[1(7 - 3) + 3(3 - 2) + 5(2 - 7)]|

= 1/2|[4 + 3 -25]|

= 1/2|[-18]|

= 1/2(18)

= 9

Therefore, area of the triangle is 9 sq. units.