Does the line through (3, 7) and (-2, -5) intersect with the line through (4, 8) and (10,-2)? (1 point)
A. No...these lines are parallel
B. Yes...these lines are perpendicular
C. No...these lines are perpendicular
D. You cannot tell without a graph
E. Yes...these lines are parallel
F. Yes...these lines are not parallel
To determine if the lines intersect, we need to find the slopes of both lines.
The slope of the line passing through (3, 7) and (-2, -5) can be calculated using the slope formula:
m = (y2 - y1) / (x2 - x1)
= (-5 - 7) / (-2 - 3)
= (-12) / (-5)
= 12/5
The slope of the line passing through (4, 8) and (10, -2) can also be calculated:
m = (-2 - 8) / (10 - 4)
= (-10) / 6
= -5/3
If the slopes of the two lines are equal, they are parallel and do not intersect.
If the slopes are negative reciprocals of each other, the lines are perpendicular and do intersect.
Comparing the slopes, 12/5 and -5/3 are neither equal nor negative reciprocals of each other. Therefore, the lines are not parallel or perpendicular.
So, the correct answer is F. Yes...these lines do not parallel.
Are you sure
I apologize, I made a mistake in my previous response.
Upon recalculating the slopes, the slope of the line passing through (3, 7) and (-2, -5) is:
m = (-5 - 7) / (-2 - 3) = -12 / -5 = 12/5
The slope of the line passing through (4, 8) and (10, -2) is:
m = (-2 - 8) / (10 - 4) = -10 / 6 = -5/3
Since the slopes are not equal and not negative reciprocals of each other, the lines are neither parallel nor perpendicular. Thus, the lines do intersect.
The correct answer is F. Yes, these lines do intersect.
To determine if the line through (3, 7) and (-2, -5) intersects with the line through (4, 8) and (10, -2), we can calculate the slopes of the two lines.
The slope of the first line can be calculated using the formula:
m1 = (y2 - y1) / (x2 - x1)
Using the given points (3, 7) and (-2, -5), we have:
m1 = (-5 - 7) / (-2 - 3)
= -12 / -5
= 12/5
The slope of the second line can be calculated using the same formula:
m2 = (y2 - y1) / (x2 - x1)
Using the given points (4, 8) and (10, -2), we have:
m2 = (-2 - 8) / (10 - 4)
= -10 / 6
= -5/3
Since the slopes of the two lines, 12/5 and -5/3, are not equal, the lines are not parallel.
Therefore, the correct answer is F. Yes, these lines are not parallel, so they may intersect.
To determine whether the lines intersect or not, we can calculate the slopes of the two lines.
The slope of a line passing through points (x1, y1) and (x2, y2) can be calculated using the formula:
slope = (y2 - y1) / (x2 - x1)
First, let's find the slope of the line passing through (3, 7) and (-2, -5):
slope1 = (-5 - 7) / (-2 - 3)
= (-12) / (-5)
= 12/5
Next, let's find the slope of the line passing through (4, 8) and (10, -2):
slope2 = (-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.
To determine whether the lines are perpendicular or not, we can check if the product of their slopes is -1. If the product of slopes is -1, the lines are perpendicular.
Product of slopes = slope1 * slope2
= (12/5) * (-5/3)
= -60/15
= -4
Since the product of the slopes is not -1, we can conclude that the lines are not perpendicular.
Therefore, the correct answer to the question "Does the line through (3, 7) and (-2, -5) intersect with the line through (4, 8) and (10,-2)?" is:
F. Yes...these lines do not intersect