Answer:
The coordinate of triangle RST from the figure are;
R = (-3,2), S=(3,2) and T=(-1,-1). also the coordinate of U = (-1, 2).
Distance Formula: It is used to determine the distance between two points with the coordinates [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] i.e,
Distance = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}[/tex]
Now, using above formula to find the sides of a given triangle:
Calculate the length of RS , where R=(-3,2) and S=(3,2);
RS=[tex]\sqrt{(3-(-3))^2+(2-2)^2}[/tex] or
RS=[tex]\sqrt{(3+3)^2+(0)^2}[/tex]
Simplify: we get
RS=[tex]\sqrt{36} =6[/tex] unit.
Similarly, for TU, where T=(-1.-1) and U=(-1,2).
then:
TU=[tex]\sqrt{(-1-(-1))^2+(2-(-1))^2}[/tex] or
TU=[tex]\sqrt{(-1+1)^2+(2+1)^2}[/tex] or
Simplify:
[tex]TU=\sqrt{0+9} =\sqrt{9} =3[/tex] unit.
Since, we have to calculate the Area of triangle RST.
To, find the area of a triangle, multiply the base by the height and then divide it by 2.
i.e,
Area of triangle = [tex]\frac{b\cdot h}{2}[/tex] where b is the base and h is the height of the triangle.
Here, in the given triangle RST, the base of the triangle = RS and the height of the triangle= TU.
Area of [tex]\triangle RST[/tex] = [tex]\frac{RS \cdot TU}{2}[/tex]
Substitute the value of RS = 6 unit and TU= 3 unit in the above formula;
Area of [tex]\triangle RST[/tex] = [tex]\frac{6\cdot3}{2}[/tex]
Simplify:
Area of [tex]\triangle RST[/tex]=[tex]3\cdot 3=9[/tex] square unit.
