Question

If the points A(1,-2), B(2,3), C(-3,2) and D(-4,-3) are the vertices of parallelogram ABCD, then taking AB as the base, find the height of this parallelogram.

Answer 1

If the points A(1,-2), B(2,3), C(-3,2) and D(-4,-3) are the vertices of parallelogram ABCD, then taking AB as the base, find the height of this parallelogram.(EC)

Solution:

1) Find length of BC:

$$B C = \sqrt {\left(x _ {2} - x _ {1}\right) ^ {2} + \left(y _ {2} - y _ {1}\right) ^ {2}}$$ $$B C = \sqrt {(- 3 - 2) ^ {2} + (2 - 3) ^ {2}} = \sqrt {2 6}$$

2) Find length of AB:

$$A B = \sqrt {\left(x _ {2} - x _ {1}\right) ^ {2} + \left(y _ {2} - y _ {1}\right) ^ {2}}$$ $$A B = \sqrt {(2 - 1) ^ {2} + (3 + 2) ^ {2}} = \sqrt {2 6}$$

3) Find length of AC:

$$A C = \sqrt {\left(x _ {2} - x _ {1}\right) ^ {2} + \left(y _ {2} - y _ {1}\right) ^ {2}}$$ $$A C = \sqrt {(- 3 - 1) ^ {2} + (2 + 2) ^ {2}} = \sqrt {3 2}$$

4) Find Angle B:

$$\cos B = \frac {B C ^ {2} + A B ^ {2} - A C ^ {2}}{2 | A B | | B C |}$$ $$\cos B = \frac {2 6 + 2 6 - 3 2}{5 2} = 0. 3 8$$

5) Find length of EC:

$$E C = B C * \sin B = B C * \sqrt {1 - \cos^ {2} B} = \sqrt {2 6} * 0. 9 2 = 4. 7 1$$

Answer: 4.71