Question

What is the area of this triangle?

A.1/2(y^3


B.


C.


D.


E.

Answer 1

D

Step-by-step explanation: plato/ edmentum answer.

Answer 2

Option: D is the correct answer.

`Area(A)=(1)/(2)(y_2-y_1)(x_3-x_1)`

Explanation:

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

`Area=(1)/(2)* base* 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=√((x_1-x_1)^2+(y_2-y_1)^2)\\\\\\Base=√(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=√((x_3-x_1)^2+(y_3-y_3)^2)\\\\\\Height=√((x_3-x_1)^2+0)\\\\\\Height=(x_3-x_1)`

Hence, the area of triangle is:

`Area=(1)/(2)(y_2-y_1)(x_3-x_1)`