If the points A(1, 2), B(3, 4), and C(5, 6) are collinear, what is the area of t
Practice Questions
Q1
If the points A(1, 2), B(3, 4), and C(5, 6) are collinear, what is the area of triangle ABC?
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Questions & Step-by-Step Solutions
If the points A(1, 2), B(3, 4), and C(5, 6) are collinear, what is the area of triangle ABC?
Correct Answer: 0
Step 1: Understand that collinear points are points that lie on the same straight line.
Step 2: Identify the coordinates of the points A(1, 2), B(3, 4), and C(5, 6).
Step 3: Use the formula for the area of a triangle given by three points (x1, y1), (x2, y2), (x3, y3): Area = 1/2 | x1(y2-y3) + x2(y3-y1) + x3(y1-y2) |.
Step 4: Substitute the coordinates into the formula: x1 = 1, y1 = 2, x2 = 3, y2 = 4, x3 = 5, y3 = 6.
Step 5: Calculate the expression inside the absolute value: 1(4-6) + 3(6-2) + 5(2-4).
Step 7: Since the result is 0, the area of triangle ABC is 1/2 * |0| = 0.
Step 8: Conclude that the area of triangle ABC is 0 because the points are collinear.
Collinearity – The concept of collinearity refers to points lying on the same straight line, which implies that the area of the triangle formed by these points is zero.
Area of a Triangle – The formula for the area of a triangle given its vertices can be used to determine the area, but if the points are collinear, the area will be zero.
