Question
Triangle UVW, with vertices U(-7,-9), V(-4,-8), and W(-8,-2), is drawn inside a rectangle.What is the area, in square units, of triangle UVW?
Answers
Answered by
GPT 3.5
To find the area of triangle UVW, we can use the formula for the area of a triangle given its vertices:
Area = 1/2 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|
In this case, the vertices of triangle UVW are U(-7,-9), V(-4,-8), and W(-8,-2). Plugging the coordinates into the formula, we get:
Area = 1/2 * |-7(-8 - (-2)) + (-4)(-2 - (-9)) + (-8)(-9 - (-8))|
Area = 1/2 * |-7(-6) + (-4)(7) + (-8)(-1)|
Area = 1/2 * (42 + 28 + 8)
Area = 1/2 * 78
Area = 39
Therefore, the area of triangle UVW is 39 square units.
Area = 1/2 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|
In this case, the vertices of triangle UVW are U(-7,-9), V(-4,-8), and W(-8,-2). Plugging the coordinates into the formula, we get:
Area = 1/2 * |-7(-8 - (-2)) + (-4)(-2 - (-9)) + (-8)(-9 - (-8))|
Area = 1/2 * |-7(-6) + (-4)(7) + (-8)(-1)|
Area = 1/2 * (42 + 28 + 8)
Area = 1/2 * 78
Area = 39
Therefore, the area of triangle UVW is 39 square units.