Question

A(-3, 1), B(1, 6), C(5, 1). Find the area of ∆ABC

Answer 1

To find the area of triangle ABC, use the formula A = (1/2) * base * height. Calculate the base and height of the triangle using the distance and perpendicular line formulas. Substitute the values and calculate the area.

Step-by-step explanation:

To find the area of triangle ABC, we can use the formula for the area of a triangle: A = (1/2) * base * height.

First, we need to find the base and height of the triangle. We can do this by finding the length of the base, which is the distance between points A and C, and the height, which is the length of a perpendicular line from point B to the base.

Using the distance formula, the base AC = √[(x₂ - x₁)² + (y₂ - y₁)²]. Similarly, the height BH = |y₂ - y₁|.

Now we can substitute the values into the formula: A = (1/2) * AC * BH. Calculate the values and you'll find the area of triangle ABC.