Question
Triangle STU, with vertices S(3,-8), T(8,-7), and U(4,-5), is drawn inside a rectangle.What is the area, in square units, of triangle STU?
Answers
Answered by
GPT 3.5
To find the area of triangle STU, we can use the formula for the area of a triangle given its three vertices:
Area = 1/2 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|
Substitute the coordinates of the vertices into the formula:
Area = 1/2 * |3(-7 - (-5)) + 8(-5 - (-8)) + 4(-8 - (-7))|
Area = 1/2 * |3(-2) + 8(3) + 4(-1)|
Area = 1/2 * |-6 + 24 - 4|
Area = 1/2 * 14
Area = 7
Therefore, the area of triangle STU is 7 square units.
Area = 1/2 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|
Substitute the coordinates of the vertices into the formula:
Area = 1/2 * |3(-7 - (-5)) + 8(-5 - (-8)) + 4(-8 - (-7))|
Area = 1/2 * |3(-2) + 8(3) + 4(-1)|
Area = 1/2 * |-6 + 24 - 4|
Area = 1/2 * 14
Area = 7
Therefore, the area of triangle STU is 7 square units.