Does the line through (3, 7) and (-2, -5) intersect with the line through (4, 8) and (10, -2)
No…these lines are parallel
You cannot tell without a graph
Yes…these lines are not parallel
Yes…these lines are perpendicular
No…these lines are perpendicular
Yes…these lines are parallel
No…these lines are parallel
To determine if two lines intersect, you can analyze their slopes. The slope of a line can be found using the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are points on the line.
Let's calculate the slopes of the two lines:
For the first line passing through (3, 7) and (-2, -5):
slope = (-5 - 7) / (-2 - 3) = -12 / -5 = 12/5
For the second line passing through (4, 8) and (10, -2):
slope = (-2 - 8) / (10 - 4) = -10 / 6 = -5/3
Since the slopes of the two lines are not equal, the lines are not parallel. However, to determine if they intersect or are perpendicular, we need to compare the slopes further.
If two lines have slopes m1 and m2, then they are perpendicular if m1 * m2 = -1. However, in this case, m1 * m2 is not equal to -1.
Therefore, we can conclude that the lines are not perpendicular either.
Hence, the correct answer is: No, these lines do not intersect.
To determine if the two lines intersect, we can calculate the slopes of both lines.
The slope of the line through (3, 7) and (-2, -5) can be found using the formula:
slope = (y2 - y1) / (x2 - x1)
slope = (-5 - 7) / (-2 - 3)
slope = -12 / -5
slope = 12/5
Similarly, the slope of the line through (4, 8) and (10, -2) can be found using the same formula:
slope = (-2 - 8) / (10 - 4)
slope = -10 / 6
slope = -5/3
Since the slopes of the two lines are different (12/5 and -5/3), the lines are not parallel.
Therefore, the answer is:
Yes, these lines are not parallel.