Find the missing side lenghts, perimeter and area of triangle ABC on the coordinates plane. All answers should be in simplest radical form, if necessary.
.A (-1,4). B (-3,2) C (0,2)
Side length AB is?
Side length BC is?
Side length AC is?
Perimeter of triangle ABC is?
Area of triangle ABC is?
To find the lengths of the sides AB, BC, and AC, we can use the distance formula:
Distance formula: √((x2 - x1)^2 + (y2 - y1)^2)
Using this formula, we can find the lengths of the sides:
AB: √((-3 - (-1))^2 + (2 - 4)^2) = √((-3 + 1)^2 + (2 - 4)^2) = √((2)^2 + (-2)^2) = √(4 + 4) = √8 = 2√2
BC: √((0 - (-3))^2 + (2 - 2)^2) = √((0 + 3)^2 + (0)^2) = √((3)^2 + (0)^2) = √9 = 3
AC: √((0 - (-1))^2 + (2 - 4)^2) = √((0 + 1)^2 + (2 - 4)^2) = √((1)^2 + (-2)^2) = √(1 + 4) = √5
So, the lengths of the sides are:
AB = 2√2
BC = 3
AC = √5
To find the perimeter, we simply add up the lengths of the sides:
Perimeter = AB + BC + AC = 2√2 + 3 + √5
To find the area of the triangle, we can use the formula for the area of a triangle:
Area = 0.5 * base * height
The base of the triangle can be found by finding the horizontal distance between points A and B, which is 2. The height can be found by finding the vertical distance from point B to the line AC, which is 2. So:
Area = 0.5 * base * height = 0.5 * 2 * 2 = 2
Therefore, the answers are:
AB = 2√2
BC = 3
AC = √5
Perimeter of triangle ABC = 2√2 + 3 + √5
Area of triangle ABC = 2.