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
3 strikes ...
1. slope AB = (2-0)/(-2-3) = -2/5
slope CD = (4+1)/(-1+3) = 5/2
So perpendicular
2. slope AB = (1+3)/(1-4) = -4/3
slope CD = (1+3)/(2-5) = -4/3
so parallel
3. slope EG = (2-0)/(-3-2) = -2/5
so slope of perpendicular is 5/2
Looks like somebody has some serious review to do.
Shut your MOUTH
To determine if two segments are parallel, perpendicular or neither, you can compare their slopes. If the slopes are equal, the segments are parallel. If the slopes are negative reciprocals of each other, the segments are perpendicular. If the slopes are neither equal nor negative reciprocals, the segments are neither parallel nor perpendicular.
Now, let's check your answers:
1.) To find the slope of segment AB, we can use the formula: slope = (change in y) / (change in x). The change in y for AB is 2 - 0 = 2, and the change in x is -2 - 3 = -5. Therefore, the slope of AB is 2 / -5 = -2/5.
Similarly, to find the slope of segment CD, we use the same formula: slope = (change in y) / (change in x). The change in y for CD is -1 - 4 = -5, and the change in x is -3 - (-1) = -3 + 1 = -2. Therefore, the slope of CD is -5 / -2 = 5/2.
Since the slopes of AB and CD are not equal, nor are they negative reciprocals of each other, the segments are neither parallel nor perpendicular. So, your answer for the first question should be "neither."
2.) To find the slope of segment AB, we can use the formula: slope = (change in y) / (change in x). The change in y for AB is 1 - (-3) = 1 + 3 = 4, and the change in x is 1 - 4 = -3. Therefore, the slope of AB is 4 / -3.
Similarly, to find the slope of segment CD, we use the same formula: slope = (change in y) / (change in x). The change in y for CD is -3 - 1 = -4, and the change in x is 5 - 2 = 3. Therefore, the slope of CD is -4 / 3.
Since the slopes of AB and CD are negative reciprocals of each other (one is the negative inverse of the other), the segments are perpendicular. So, your answer for the second question is correct.
3.) To find the slope of segment EG, we can use the formula: slope = (change in y) / (change in x). The change in y for EG is 0 - 2 = -2, and the change in x is 2 - (-3) = 2 + 3 = 5. Therefore, the slope of EG is -2 / 5 = -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 EG is the negative reciprocal of -2/5, which is 5/2.
Therefore, your answer for the third question is incorrect. The correct slope of the line perpendicular to segment EG is 5/2.
Keep in mind that it's always a good idea to double-check your work and calculations.