Question

Find the horizontal and vertical components of directed line segment PQ to the left.

- a) Horizontal: (|PQ| ⋅ cos(θ)), Vertical: (|PQ| ⋅ sin(θ))
- b) Horizontal: (|PQ| ⋅ sin(θ)), Vertical: (|PQ| ⋅ cos(θ))
- c) Horizontal: (|PQ| ⋅ tan(θ)), Vertical: (|PQ| ⋅ cot(θ))
- d) Horizontal: (|PQ| ⋅ cot(θ)), Vertical: (|PQ| ⋅ tan(θ))

Find the horizontal and vertical components of directed line segment CD with coordinates C(-2, 6) and D(1,-1).
- a) Horizontal: 3, Vertical: -7
- b) Horizontal: -3, Vertical: 7
- c) Horizontal: 4, Vertical: -5
- d) Horizontal: -4, Vertical: 5

Answer 1

The horizontal component of directed line segment CD is 3, and the vertical component is -7, obtained by subtracting the coordinates of points C and D.

Step-by-step explanation:

To find the horizontal and vertical components of a directed line segment, we can use trigonometric functions if an angle is given, or simple subtraction if we are given the coordinates of the endpoints. In this case, we are dealing with the coordinates of points C(-2, 6) and D(1, -1).

The horizontal component is the difference in the x-coordinates of D and C, which is 1 - (-2) = 3. The vertical component is the difference in the y-coordinates of D and C, which is -1 - 6 = -7.

Therefore, the answer for the horizontal and vertical components of directed line segment CD is a) Horizontal: 3, Vertical: -7.