Question

The area of the triangle with vertices (1,1),(2,2) and (−3,1) is 1) 1 2) 2 3) 3 4) 4

Answer 1

Answer:

area of the triangle is 2

Answer 2

Given data: The vertices of a triangle are (1,1), (2,2) and (-3,1).

To Find: The area of a triangle.

Solution:

Consider the vertices, $(x_{1},y_{1})=(1,1)$, $(x_{2},y_{2})=(2,2)$ and $(x_{3},y_{3} )=(-3,1)$

Area of a triangle $=\frac{1}{2}[x_{1}(y_{2 }-y_{3})+x_{2}(y_{3}-y_{1})+x_{3}(y_{1}-y_{2})]$

Substitute, $x_{1}=1, x_{2}=2, x_{3}=-3, y_{1}=1, y_{2}=2, y_{3}=1$ in the formula.

Area of a triangle$=\frac{1}{2}[1(2-1)+2(1-1)+(-3)(1-2)]$

$=\frac{1}{2}(1+0+3)$

$=\frac{1}{2}(4)$

$=\frac{4}{2}$

$=2$

Therefore, area of a triangle with vertices (1,1), (2,2), (-3,1) is (2) 2 square units.