Question

1. which of the following lines is horizontal? a. x = 3 b. y = 3x c. y = 3 d. x + y = 3 14. for which purpose is the distance formula particularly important in robotics? a. sensor tuning b. power management c. navigating between points d. signal processing 15. are two lines perpendicular if their slopes are 1/2 and - 4? a. yes b. no c. it depends on the points d. not enough information

Explanation:

Step1: Recall horizontal - line equation

The equation of a horizontal line is of the form $y = k$, where $k$ is a constant.

Step2: Analyze each option

• Option a: $x = 3$ is a vertical line.
• Option b: $y = 3x$ is a line with slope 3, not horizontal.
• Option c: $y = 3$ is of the form $y=k$ (where $k = 3$), so it is a horizontal line.
• Option d: $x + y=3$ can be rewritten as $y=-x + 3$, which is a non - horizontal line.

Step3: Recall the use of distance formula in robotics

The distance formula is used to find the distance between two points. In robotics, it is crucial for navigating between points. Sensor tuning is related to calibration of sensors, power management is about energy consumption, and signal processing is about handling sensor signals.

Step4: Recall the condition for perpendicular lines

Two lines with slopes $m_1$ and $m_2$ are perpendicular if $m_1\times m_2=- 1$. If $m_1=\frac{1}{2}$ and $m_2=-4$, then $m_1\times m_2=\frac{1}{2}\times(-4)=-2
eq - 1$.

Answer:

1. C. $y = 3$
2. C. Navigating between points
3. B. No