Question

ABC is a right triangle in the coordinate plane with a right angle at vertex B. The vertices of the triangle are A(18,7), B(8,3), and C(6,13). Find the area of ABC.

A) 32 square units

B) 48 square units

C) 56 square units

D) 64 square units

Answer 1

To find the area of triangle ABC, use the formula for the area of a triangle. Calculate the base and height, then substitute them into the formula to find the area.

Step-by-step explanation:

To find the area of the triangle ABC, we can use the formula for the area of a triangle: A = (1/2) * base * height. In this case, the base of the triangle is the distance between points B and C, and the height of the triangle is the perpendicular distance from point A to line BC.

Using the coordinates of the three points, we can find the length of BC using the distance formula: BC = sqrt((Cx - Bx)^2 + (Cy - By)^2). Then, we can calculate the perpendicular distance from point A to line BC using the formula: distance = abs(Ax * (By - Cy) + Bx * (Cy - Ay) + Cx * (Ay - By)) / sqrt((By - Cy)^2 + (Cx - Bx)^2).

Finally, we can substitute the values into the formula for the area of a triangle to get the result.