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

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Ashleyvasquez8414idn Ashleyvasquez8414idn

06-01-2021
Mathematics

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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

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Sqdancefanidn Sqdancefanidn · Answer 1 · 2021-01-06T21:59:09-05:00

9514 1404 393

Answer:

18 square units

Step-by-step 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.

_____

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

DragonWriteridn DragonWriteridn · Answer 2 · 2021-06-23T08:05:45-04:00

DragonWriteridn DragonWriteridn

23-06-2021

Answer:

B: 18 square units

Step-by-step explanation:

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