Question

What is the area of this triangle?

Answer 1

Answer: C

Step-by-step explanation:

Answer 2

Answer:

Option: D is the correct answer.

             $Area(A)=\dfrac{1}{2}(y_2-y_1)(x_3-x_1)$

Step-by-step explanation:

We know that the area of a triangle is given by the formula:

$Area=\dfrac{1}{2}\times base\times height$

Here in this figure we have a base as a line segment joining,

$(x_1,y_1)\ \text{and}\ (x_1,y_2)$

Hence, the measure of length of base is:

$Base=\sqrt{(x_1-x_1)^2+(y_2-y_1)^2}\\\\\\Base=\sqrt{0+(y_2-y_1)^2}\\\\\\Base=(y_2-y_1)$

and height is a line segment joining,

$(x_1,y_3)\ \text{and}\ (x_3,y_3)$

Hence, measure of height of triangle is:

$Height=\sqrt{(x_3-x_1)^2+(y_3-y_3)^2}\\\\\\Height=\sqrt{(x_3-x_1)^2+0}\\\\\\Height=(x_3-x_1)$

              Hence, the area of triangle is:

           $Area=\dfrac{1}{2}(y_2-y_1)(x_3-x_1)$