Question

The vertices of triangle ABC have coordinates A(-2,-1) B(10,-1) and C(4,4). Determine and state the area of triangle ABC

Answer 1

To determine the area of triangle ABC, you can use the formula for the area of a triangle: A = 1/2 * base * height. In this case, you can use the distance formula to find the lengths of the base and height.

Step-by-step explanation:

To determine the area of triangle ABC, you can use the formula for the area of a triangle: A = 1/2 * base * height. In this case, you can use the distance formula to find the lengths of the base and height.

The distance between points A and B is the base, so you can use the formula: Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2). Substituting the coordinates of A and B, you get Distance = sqrt((-3 - 2)^2 + (3 - (-4))^2) = sqrt(25 + 49) = sqrt(74).

The height of the triangle is the distance between point C and a line containing the base. You can find the equation of the line containing AB and then use the formula for the distance between a point and a line: Distance = |Ax + By + C| / sqrt(A^2 + B^2). Substituting the coordinates of A, B, and C into the formula, you can find the equation of the line and calculate the distance.

Once you have the base and height, you can calculate the area of the triangle using the formula: A = 1/2 * base * height.

Answer 2

Area = 1/2 * base * height

Base = A to B = 10 - (-2) = 12

Height = C down = 4 - (-1) = 5

Area = 1/2 * 12 * 5
Area = 1/2 * 60
Area = 30