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Triangle UVW, with vertices U(-5,-9), V(-2,-5), and W(-8,-4), is drawn on the coordinate grid below. What is the area, in square units, of triangle UVW?

a) 12 square units
b) 10 square units
c) 18 square units
d) 8 square units

User Thpitsch
by
7.3k points

1 Answer

6 votes

Final answer:

To calculate the area of triangle UVW with given vertices, we use the determinant method and find that the area is 31 square units, which conflicts with the provided choices, indicating a possible error.

Step-by-step explanation:

The subject of the question involves calculating the area of a triangle on the coordinate grid using the coordinates of its vertices. To find the area of the triangle UVW with vertices U(-5,-9), V(-2,-5), and W(-8,-4), we can use the shoelace formula or the determinant method.

The formula for the area of a triangle given coordinates is:

Area = 0.5 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|

Applying the formula and plugging in the coordinates:

Area = 0.5 * |-5(-5 + 4) - 2(-4 + 9) - 8(-9 + 5)|
= 0.5 * |20 + 10 + 32|
= 0.5 * 62
= 31

The error in the options given indicates that the correct area should be 31 square units, which is not listed among the provided choices.

User Ruhig Brauner
by
8.6k points
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