Triangle ABC, with vertices A(8,2), B(7,9), and C(3,6), is drawn inside a rectangle, as shown below.What is the area, in square units, of triangle ABC?
First, we need to find the lengths of the sides of triangle ABC.
Using the distance formula:
AB = √((7-8)^2 + (9-2)^2) = √(1^2 + 7^2) = √(1 + 49) = √50
BC = √((3-7)^2 + (6-9)^2) = √(4^2 + 3^2) = √(16 + 9) = √25 = 5
AC = √((3-8)^2 + (6-2)^2) = √(5^2 + 4^2) = √(25 + 16) = √41
Now, we can use Heron's formula to find the area of triangle ABC:
s = (AB + BC + AC)/2
s = (√50 + 5 + √41)/2
s = (7.07 + 5 + 6.40)/2
s = 18.47/2
s = 9.235
Area = √(s(s-AB)(s-BC)(s-AC))
Area = √(9.235(9.235-√50)(9.235-5)(9.235-√41))
Area = √(9.235(9.235-7.07)(9.235-5)(9.235-6.40))
Area = √(9.235(2.165)(4.235)(2.835))
Area = √(67.033 * 2.835)
Area = √189.991
Area ≈ 13.78 square units
Therefore, the area of triangle ABC is approximately 13.78 square units.
THIS ISNT THE RIGHT ANSWER
I apologize for the oversight. Let's try calculating the area of triangle ABC again.
We can use the formula for the area of a triangle given its coordinates:
Area = 0.5 * |(x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2))|
Substitute the coordinates of A(8,2), B(7,9), and C(3,6) into the formula:
Area = 0.5 * |(8(9-6) + 7(6-2) + 3(2-9))|
Area = 0.5 * |(8(3) + 7(4) + 3(-7))|
Area = 0.5 * |(24 + 28 - 21)|
Area = 0.5 * |31|
Area = 0.5 * 31
Area = 15.5 square units
Therefore, the area of triangle ABC is 15.5 square units. Thank you for bringing this to my attention.
Triangle ABC, with vertices A(-4,-9), B(-2,-3), and C(-8,-4), is drawn inside a rectangle, as shown below.What is the area, in square units, of triangle ABC?
To find the area of triangle ABC with vertices A(-4, -9), B(-2, -3), and C(-8, -4), we can use the formula for the area of a triangle given its coordinates:
Area = 0.5 * |(x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2))|
Substitute the coordinates of the given vertices into the formula:
Area = 0.5 * |(-4(-3 - (-4)) + (-2(-4 - (-9)) + (-8(-9 - (-3)))|
Area = 0.5 * |(-4(1) + 2(-5) + 8(-6))|
Area = 0.5 * |(-4 - 10 - 48)|
Area = 0.5 * |-62|
Area = 31
Therefore, the area of triangle ABC is 31 square units.
THIS ISNT THE RIGHT ANSWER
Let's correct the calculation for the area of triangle ABC using the formula for the area of a triangle given its coordinates:
Area = 0.5 * |(x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2))|
Given vertices A(-4, -9), B(-2, -3), and C(-8, -4), substituting the coordinates into the formula:
Area = 0.5 * |(-4(-3 - (-4)) + (-2(-4 - (-9)) + (-8(-9 - (-3)))|
Area = 0.5 * |(-4(1) + 2(5) + 8(-6))|
Area = 0.5 * |(-4 + 10 - 48)|
Area = 0.5 * |-42|
Area = 21
Therefore, the corrected area of triangle ABC is 21 square units.