Area of a Triangle (Leaving Cert Mathematics): Quizzes

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Area of a Triangle
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What is the formula for area of triangle with one vertex at origin?

12∣x1y2−x2y1∣\frac{1}{2}|x_1y_2 - x_2y_1|

When can you use the formula 12∣x1y2−x2y1∣\frac{1}{2}|x_1y_2 - x_2y_1| directly?

When one vertex is at origin (0,0)

Why do we use absolute value in the area formula?

To ensure area is always positive

What does 'cross multiplication' mean in this formula?

Multiply x1x_1 by y2y_2 and x2x_2 by y1y_1

When must you translate a triangle?

When no vertex is at the origin

Does translation change the area of a triangle?

No, area stays the same

Find area of triangle with vertices (0,0), (-2,1), (3,4).

5.5 square units

To translate (2,4) to origin, what do you do to all vertices?

Subtract 2 from x's, 4 from y's

What is the final step in calculating the area?

Multiply by 12\frac{1}{2}

Which common mistake makes the area negative?

Forgetting absolute value

What happens if you forget to multiply by 12\frac{1}{2}?

Area is double the correct value

Can you choose any vertex to move to the origin?

Yes, result will be the same

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