Question

Triangle UVW, with vertices U(-7,-9), V(-4,-7), and W(-6,-6), is drawn on the coordinate grid below

Answer 1

We must compute the area of a triangle with vertices:

• P1 = (x1, y1) = U = (-7, -9),

,

• P2 = (x2, y2) = V = (-4, -7),

,

• P3 = (x3, y3) = W = (-6, -6).

The area of a triangle given the coordinates of its vertices is given by the following formula:

$A=\frac{1}{2}\cdot|x_1\cdot(y_2-y_3)+x_2\cdot(y_3-y_1)+x_3\cdot(y_1-y_2)|\text{.}$

Replacing the values of the coordinates in the formula above, we get:

$A=\frac{1}{2}\cdot|(-7)\cdot(-7+6)+(-4)\cdot(-6+9)+(-6)\cdot(-9+7)|=\frac{7}{2}=3.5.$

Answer

The area in square units of the triangle UVW is 3.5.