Question

Calculate the area of triangle ABC with altitude CD, given A(−7, −1), B(−1, 5), C(0, 0), and D(−3, 3). 9 square units 18 square units 18.5 square units 21 square units

Answer 1

B: 18 square units

Explanation:

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Answer 2

9514 1404 393

Answer:

18 square units

Explanation:

Referring to the figure, we see that the base AB has a slope of 1, and the altitude CD has a slope of -1. The number of unit squares crossed by these segments are, respectively 6 and 3, so the length of each is ...

AB = 6√2

CD =3√2

The area is half the product of the base (AB) and height (CD) so is ...

A = 1/2bh = (1/2)(6√2)(3√2) = 18

The area of ΔABC is 18 square units.

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Additional comment

It is useful to remember that the diagonal of a unit square is √2. We used that fact here. If you need to figure it using the Pythagorean theorem, you find ...

c² = a² +b²

c = 1² +1² = 2

c = √2