Question

what is the area of △uvw?
coordinate grid with points u, v, w plotted
area = \square square units

Explanation:

Step1: Find the base length

Points U and V are on the line \( y = 8 \). The x - coordinate of U is - 5 (assuming each grid is 1 unit, from the graph: U is at (-5,8), V is at (4,8)). The length of UV (base) is \( |4 - (-5)|=9 \) units.

Step2: Find the height

The height is the vertical distance from point W to the line UV. Point W is at (2,10), and the y - coordinate of UV is 8. So the height \( h=10 - 8 = 2 \) units.

Step3: Calculate the area of the triangle

The formula for the area of a triangle is \( A=\frac{1}{2}\times base\times height \). Substituting base = 9 and height = 2, we get \( A=\frac{1}{2}\times9\times2 \).
\( \frac{1}{2}\times9\times2=9 \)

Answer:

9