Find the area of the triangle whose vertices are (3,8),(−4,2) and (5,1).
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Step-by-Step Solution
Step 1: Identify the coordinates
First, we identify the coordinates of the three vertices of the triangle. Let's label them as A, B, and C with their respective (x, y) coordinates.
Step 2: Recall the area formula
The area of a triangle with vertices (x1,y1), (x2,y2), and (x3,y3) can be calculated using this determinant-based formula. The absolute value ensures the area is always positive.
Step 3: Substitute the coordinates
Now, we substitute the coordinates of the vertices into the area formula. We replace x1,y1,x2,y2,x3,y3 with their respective numerical values.
Step 4: Calculate the expression
Next, we perform the subtractions inside the parentheses and then the multiplications. This simplifies the expression within the absolute value.
Step 5: Simplify and find the area
Finally, we sum the terms inside the absolute value and multiply by 21 to get the area of the triangle. The area is 30.5 square units.