HOW CAN YOU DETERMINE IT TWO LINES ARE PERPENDICUAR?
To determine if two lines are perpendicular, you need to check if the slopes of the lines are negative reciprocals of each other. Here's how you can determine this:
1. Find the slopes of the two lines:
- Given the equation of a line in the form y = mx + b, the slope (m) is the coefficient of the x-term.
- For example, if Line 1 has the equation y = 2x + 3, its slope is 2.
- Similarly, if Line 2 has the equation y = -1/2x + 2, its slope is -1/2.
2. Take the negative reciprocal of the slope of Line 1:
- Flip the fraction and change its sign.
- For Line 1 with a slope of 2, the negative reciprocal is -1/2.
- For Line 2 with a slope of -1/2, the negative reciprocal is 2.
3. Compare the slopes:
- If the slopes of the two lines are equal to the negative reciprocal of each other, the lines are perpendicular.
- In our example, the slopes of Line 1 (2) and Line 2 (-1/2) are negative reciprocals of each other, so the lines are perpendicular.
Remember that if the lines are not given by equations, you may need other methods to find their slopes, such as using their coordinates or determining them from the given angles.