Calculate the area of triangle ABC with altitude CD, given A (−3, −4), B (−6, 2), C (0, 0), and D (−4, −2). a. 14 square units b

Question

kirill115 [55]

2 years ago

10

Calculate the area of triangle ABC with altitude CD, given A (−3, −4), B (−6, 2), C (0, 0), and D (−4, −2). a. 14 square units b

. 15 square units c. 18 square units d. 20 square units

Mathematics

1 answer:

babymother [125] · Answer 1 · 2022-10-13T10:34:09+03:00

Answer:

b. 15 square units

Step-by-step explanation:

We notice from the graph that AB is the hypotenuse of a right triangle 3 units wide and 6 units high. The Pythagorean theorem tells you the length of that will be ...

AB = √(3^2 +6^2) = √45 = 3√5

Similarly, altitude CD is the hypotenuse of a right triangle 4 units wide and 2 units high, so its length will be ...

CD = √(4^2 +2^2) = √20 = 2√5

The area is given by the formula ...

A = 1/2bh

A = 1/2(3√5)(2√5) = 15 . . . square units