To find the side lengths AB, BC, and AC, we will use the distance formula between two points in a coordinate plane: √((x2 - x1)² + (y2 - y1)²)
Side Length AB (between points A(-1, 4) and B(-3, 2)):
AB = √((-3 - (-1))² + (2 - 4)²)
AB = √((-2)² + (-2)²)
AB = √(4 + 4)
AB = √8
AB = 2√2
Side Length BC (between points B(-3, 2) and C(0, 2)):
BC = √((0 - (-3))² + (2 - 2)²)
BC = √(3² + 0²)
BC = √9
BC = 3
Side Length AC (between points A(-1, 4) and C(0, 2)):
AC = √((0 - (-1))² + (2 - 4)²)
AC = √(1² + (-2)²)
AC = √(1 + 4)
AC = √5
Perimeter of Triangle ABC:
Perimeter = AB + BC + AC
Perimeter = 2√2 + 3 + √5
Area of Triangle ABC (with base BC and height from A to BC):
The height can be calculated as the difference in the y-coordinates of point A and line BC, which is:
Height = y(A) - y(C) = 4 - 2 = 2
Using the area formula A = (b * h) / 2, where b is the base (BC) and h is the height:
Area = (BC * Height) / 2
Area = (3 * 2) / 2
Area = 3
Now, let's input the results to the appropriate fields.
Side Length AB: 2√2
Side Length BC: 3
Side Length AC: √5
Perimeter of Triangle ABC: 2√2 + 3 + √5
Area of Triangle ABC: 3
Question
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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.:
a is (-1,4)
b is (-3,2)
c is (0,2)
Side Length AB:
Side Length BC:
Side Length AC:
Perimeter of Triangle ABC:
Area of Triangle ABC: Response area
Note: the formula for area of a triangle is A=bh2
, where b is the length of the base (BC) and h is the height from side BC to point A.
1 answer