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

2 Answers
Oct 18, 2017

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.

Oct 18, 2017

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."