Hello! I wanted to know if my answers are right or not? Thanks! :)
1.) Segments AB and CD have the following endpoints. Determine whether the segments are parallel, perpendicular or neither. A (3, 0), B (-2, 2), C (-1, 4), D (-3, -1)
My answer: Parallel
2.) Segments AB and CD have the following endpoints. Determine whether the segments are parallel, perpendicular or neither. A (4, -3), B (1, 1), C (2, 1), D (5, -3)
My answer: Perpendicular
3.) What is the slope of the line perpendicular to Segment EG if the coordinates are (-3, 2) and (2, 0)?
My answer: 2/5
Let's go through each question and verify your answers.
1.) Segments AB and CD have the following endpoints. Determine whether the segments are parallel, perpendicular or neither. A (3, 0), B (-2, 2), C (-1, 4), D (-3, -1)
To determine if segments AB and CD are parallel, perpendicular, or neither, we can calculate the slopes of the two segments. The formula for finding the slope between two points (x1, y1) and (x2, y2) is (y2 - y1) / (x2 - x1).
For segment AB: slope_AB = (2 - 0) / (-2 - 3) = 2 / -5 = -2/5
For segment CD: slope_CD = (-1 - 4) / (-3 - (-1)) = -5 / -2 = 5/2
Since the slopes of the two segments are different, AB and CD are neither parallel nor perpendicular.
Your answer for question 1 is incorrect. The correct answer is: Neither.
2.) Segments AB and CD have the following endpoints. Determine whether the segments are parallel, perpendicular, or neither. A (4, -3), B (1, 1), C (2, 1), D (5, -3)
Again, we can find the slopes of segment AB and CD:
For segment AB: slope_AB = (1 - (-3)) / (1 - 4) = 4 / (-3) = -4/3
For segment CD: slope_CD = (1 - 1) / (2 - 5) = 0 / (-3) = 0
The slope of segment AB is -4/3, and the slope of segment CD is 0. Two lines are perpendicular if and only if their slopes are negative reciprocals of each other. Since -4/3 is the negative reciprocal of 0, we can conclude that AB and CD are perpendicular.
Your answer for question 2 is correct: Perpendicular.
3.) What is the slope of the line perpendicular to Segment EG if the coordinates are (-3, 2) and (2, 0)?
First, let's find the slope of segment EG:
slope_EG = (0 - 2) / (2 - (-3)) = -2 / 5
The slope of the line perpendicular to EG will be the negative reciprocal of the slope of EG. Therefore, the slope of the perpendicular line is 5/2.
Your answer for question 3 is incorrect. The correct answer is: 5/2.
I hope this clarifies your doubts. Let me know if you have any other questions!
To determine whether two segments are parallel, perpendicular, or neither, you need to consider the slopes of the lines containing the segments.
1.) For the given endpoints A (3, 0), B (-2, 2), C (-1, 4), and D (-3, -1), we can find the slopes of segments AB and CD. The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula: slope = (y₂ - y₁) / (x₂ - x₁).
For segment AB, the slope is (2 - 0) / (-2 - 3) = 2 / (-5) = -2/5.
For segment CD, the slope is (-1 - 4) / (-3 - (-1)) = -5 / (-2) = 5/2.
Since the slopes of segments AB and CD are not equal, they are not parallel. Therefore, the answer is neither.
2.) For the given endpoints A (4, -3), B (1, 1), C (2, 1), and D (5, -3), we can find the slopes of segments AB and CD.
For segment AB, the slope is (1 - (-3)) / (1 - 4) = 4 / (-3) = -4/3.
For segment CD, the slope is (1 - 1) / (2 - 5) = 0 / (-3) = 0.
The slopes of segments AB and CD are not equal and their product is -4/3 * 0 = 0. Therefore, the segments are perpendicular.
3.) To find the slope of the line perpendicular to segment EG, we first need to find the slope of segment EG. Given the endpoints (-3, 2) and (2, 0), the slope is (0 - 2) / (2 - (-3)) = -2 / 5.
The slope of a line perpendicular to another line is the negative reciprocal of its slope. So, the slope of the line perpendicular to segment EG is the negative reciprocal of -2/5, which is 5/2.
Therefore, your answer of 2/5 is incorrect. The correct answer is 5/2.