Does the line through (3, 7) and (-2, -5) intersect with the line through (4, 8) and (10, -2)?(1 point)
No…these lines are parallel
Yes…these lines are not parallel
You cannot tell without a graph
Yes…these lines are perpendicular
Yes…these lines are parallel
No…these lines are perpendicular
You cannot tell without a graph.
To determine if the lines intersect or not, we need to find the slopes of both lines. The slope of a line passing through two points (x1, y1) and (x2, y2) can be calculated using the formula:
slope = (y2 - y1) / (x2 - x1)
Let's calculate the slope of the first line passing through (3, 7) and (-2, -5):
slope1 = (-5 - 7) / (-2 - 3)
= (-12) / (-5)
= 12 / 5
Now, let's calculate the slope of the second line passing through (4, 8) and (10, -2):
slope2 = (-2 - 8) / (10 - 4)
= (-10) / 6
= -5/3
Since the slopes are not equal, the lines are not parallel. However, to determine if they are perpendicular or intersecting, we need to check if the product of their slopes is -1.
slope1 * slope2 = (12/5) * (-5/3)
= -12/3
= -4
The product of the slopes is not equal to -1. Therefore, the lines are not perpendicular either.
In conclusion, the correct answer is: No...these lines are not parallel.
To determine whether the lines intersect, we can calculate the slopes of both lines. If the slopes are equal, the lines are parallel and do not intersect. If the slopes are negative reciprocals of each other, the lines are perpendicular and do intersect. If the slopes are neither equal nor negative reciprocals, then the lines are neither parallel nor perpendicular, and we cannot determine if they intersect without a graph or additional information.
The formula to calculate the slope between two points (x1, y1) and (x2, y2) is given by:
m = (y2 - y1) / (x2 - x1)
Let's calculate the slope of the first line using the points (3, 7) and (-2, -5):
m1 = (-5 - 7) / (-2 - 3)
= -12 / -5
= 12/5
Similarly, let's calculate the slope of the second line using the points (4, 8) and (10, -2):
m2 = (-2 - 8) / (10 - 4)
= -10 / 6
= -5/3
Since the slopes of the two lines are not equal, we can conclude that the lines are not parallel. However, their slopes are also not negative reciprocals of each other, so they are not perpendicular either. Therefore, we cannot determine if the lines intersect without a graph or additional information. The correct answer is: "You cannot tell without a graph."