Question

The vertices of triangle ABC are A(-4,0), B(2,4), and C(4,0). What is its area?

Answer 1

`16un.^2`

Explanation:

Don"t be intimidated by the points. Graph them and find your base and height

This is easy because your base is just the distance from A to A on the horizontal plane, 8.
The height is defined by the vertical distance of B, 4.

Now use the area of a triangle formula (A = `1/2*b*h`)
A = `1/2(4)(8)`
A = `1/2 * 32`
A = 16

Your area is 16 sq. units.

Answer 2

`16" sq. units."`

Explanation:

Let us denote, by `[ABC],` the Area of a `DeltaABC.`

We know from the Co-ordinate Geometry, that, if the vertices of

`DeltaABC` are `A(x_1,y_1), B(x_2,y_2), and, C(x_3,y_3),` then,

`[ABC]=1/2*|D|," where, "D=|(x_1,y_1,1),(x_2,y_2,1),(x_3,y_3,1)|.`

Here, `D=|(-4,0,1),(2,4,1),(4,0,1)|,`

`=-4(4xx1-0xx1)-0+1(2xx0-4xx4),`

`=-4(4)+1(-4),`

`rArr D=-32.`

`"Therefore, "[ABC]=1/2*|-32|=16" sq.units."`