Question

What is the area of this triangle

Answer 1

The area of the triangle is 1/2 times the product of the base length
`(x_3 - x_1)`and the height
`(y_3 - y_1)`. So, A =
`(1)/(2)(y_3 - y_1)(x_3 - x_1)`. Option B is the right choice.

The base of the triangle is the horizontal side, with vertices at (
`x_1, y_1`) and (
`x_3, y_3`).

The height of the triangle is the vertical distance from the top vertex (
`x_3, y_3`) to the base.

Calculate the length of the base:

Subtract the x-coordinates of the base's endpoints: base =
`x_3 - x_1`

Calculate the height:

Subtract the y-coordinates of the top vertex and the endpoint of the base that shares the same x-coordinate: height =
`y_3 - y_1`

Apply the formula for the area of a triangle:

Area = 1/2 * base * height.

Substitute the calculated values: Area = 1/2 *
`(x_3 - x_1)` *
`(y_3 - y_1)`

Therefore, the correct area formula for this triangle is option B: A =
`(1)/(2)(y_3 - y_1)(x_3 - x_1)`