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
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