Question
Provide the correct answers and Find the missing side lengths, perimeter, and area of triangle ABC on the coordinate plane. All answers should be in simplest radical form, if necessary:
Side length AB:
Side length BC:
Side length AC:
Perimeter of triangle ABC:
Area of triangle ABC:
a is: A = (-1,4)
b is: B = (-3,2)
c is: C = (0,2)
Note: the formula for the area of a triangle is A = bh/2, where b is the length of the base (BC) and h is the height from side BC to point A.
Answer choices
A. 2√2
B. 2
C. 3
D. √3
E. √5
F. 5
G. √8
H. 3 + 2√2 + √5
I. 7 + √8
Side length AB:
Side length BC:
Side length AC:
Perimeter of triangle ABC:
Area of triangle ABC:
a is: A = (-1,4)
b is: B = (-3,2)
c is: C = (0,2)
Note: the formula for the area of a triangle is A = bh/2, where b is the length of the base (BC) and h is the height from side BC to point A.
Answer choices
A. 2√2
B. 2
C. 3
D. √3
E. √5
F. 5
G. √8
H. 3 + 2√2 + √5
I. 7 + √8
Answers
GPT 3.5
To find the side lengths of triangle ABC, we can use the distance formula.
Side length AB:
AB = √((x2 - x1)^2 + (y2 - y1)^2)
AB = √((-3 - (-1))^2 + (2 - 4)^2)
AB = √((-3 + 1)^2 + (2 - 4)^2)
AB = √((-2)^2 + (-2)^2)
AB = √(4 + 4)
AB = √8
Side length BC:
BC = √((x2 - x1)^2 + (y2 - y1)^2)
BC = √((0 - (-3))^2 + (2 - 2)^2)
BC = √((0 + 3)^2 + 0^2)
BC = √(3^2 + 0)
BC = √(9 + 0)
BC = √9
BC = 3
Side length AC:
AC = √((x2 - x1)^2 + (y2 - y1)^2)
AC = √((0 - (-1))^2 + (2 - 4)^2)
AC = √((0 + 1)^2 + (-2)^2)
AC = √(1 + 4)
AC = √5
Now, let's calculate the perimeter of triangle ABC.
Perimeter = AB + BC + AC
Perimeter = √8 + 3 + √5
Finally, let's calculate the area of triangle ABC using the formula A = bh/2.
The base of the triangle is BC, which is 3.
The height is the y-coordinate of point A, which is 4.
Area = (3 * 4)/2 = 12/2 = 6
So, the answers are:
Side length AB: √8
Side length BC: 3
Side length AC: √5
Perimeter of triangle ABC: √8 + 3 + √5
Area of triangle ABC: 6
Side length AB:
AB = √((x2 - x1)^2 + (y2 - y1)^2)
AB = √((-3 - (-1))^2 + (2 - 4)^2)
AB = √((-3 + 1)^2 + (2 - 4)^2)
AB = √((-2)^2 + (-2)^2)
AB = √(4 + 4)
AB = √8
Side length BC:
BC = √((x2 - x1)^2 + (y2 - y1)^2)
BC = √((0 - (-3))^2 + (2 - 2)^2)
BC = √((0 + 3)^2 + 0^2)
BC = √(3^2 + 0)
BC = √(9 + 0)
BC = √9
BC = 3
Side length AC:
AC = √((x2 - x1)^2 + (y2 - y1)^2)
AC = √((0 - (-1))^2 + (2 - 4)^2)
AC = √((0 + 1)^2 + (-2)^2)
AC = √(1 + 4)
AC = √5
Now, let's calculate the perimeter of triangle ABC.
Perimeter = AB + BC + AC
Perimeter = √8 + 3 + √5
Finally, let's calculate the area of triangle ABC using the formula A = bh/2.
The base of the triangle is BC, which is 3.
The height is the y-coordinate of point A, which is 4.
Area = (3 * 4)/2 = 12/2 = 6
So, the answers are:
Side length AB: √8
Side length BC: 3
Side length AC: √5
Perimeter of triangle ABC: √8 + 3 + √5
Area of triangle ABC: 6