Answer:
Option: D is the correct answer.
[tex]Area(A)=\dfrac{1}{2}(y_2-y_1)(x_3-x_1)[/tex]
Step-by-step explanation:
We know that the area of a triangle is given by the formula:
[tex]Area=\dfrac{1}{2}\times base\times height[/tex]
Here in this figure we have a base as a line segment joining,
[tex](x_1,y_1)\ \text{and}\ (x_1,y_2)[/tex]
Hence, the measure of length of base is:
[tex]Base=\sqrt{(x_1-x_1)^2+(y_2-y_1)^2}\\\\\\Base=\sqrt{0+(y_2-y_1)^2}\\\\\\Base=(y_2-y_1)[/tex]
and height is a line segment joining,
[tex](x_1,y_3)\ \text{and}\ (x_3,y_3)[/tex]
Hence, measure of height of triangle is:
[tex]Height=\sqrt{(x_3-x_1)^2+(y_3-y_3)^2}\\\\\\Height=\sqrt{(x_3-x_1)^2+0}\\\\\\Height=(x_3-x_1)[/tex]
Hence, the area of triangle is:
[tex]Area=\dfrac{1}{2}(y_2-y_1)(x_3-x_1)[/tex]
