Answer:
Option B is correct.
The area of triangle GHJ is, 6 square units.
Explanation:
Given: In ΔGHJ
the coordinates are G=(1,1) , H=(4,1) and J=(4,5).
Now, find the length of GH and HJ by using distance(D) formula for two points [tex](x_1 ,y_1)[/tex] and [tex](x_2 ,y_2)[/tex] is given by:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Calculate the length of GH;
GH = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] = [tex]\sqrt{(4-1)^2+(1-1)^2}= \sqrt{(3)^2+(0)^2}=\sqrt{9} =3[/tex] unit
Similarly, for the length of HJ;
HJ = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] = [tex]\sqrt{(4-4)^2+(5-1)^2}= \sqrt{(0)^2+(4)^2}=\sqrt{16} =4[/tex] unit
Using formula for the area of a triangle is
[tex]A=\frac{1}{2}bh[/tex]; where b is the base and h is the height.
then; the area of triangle GHJ; [tex]A=\frac{1}{2} (GH)(HJ)[/tex] where GH represents the base and HJ represents the height.
Substituting the values of GH and HJ in above formula:
[tex]A=\frac{1}{2} \cdot 3 \cdot 4 =3 \cdot 2 =6[/tex] square units.
Therefore, the area of ΔGHJ is, 6 square units.
