Does the line through (3, 7) and (-2, -5) intersect with the line through (4, 8) and (10, -2)?
• No...these lines are parallel
O Yes...these lines are parallel
O You cannot tell without a graph
Yes... these lines are not parallel
• Yes...these lines are perpendicular
O No.. these lines are perpendicular
No...these lines are parallel
To determine if the lines intersect or not, we can check if the slopes of the two lines are equal.
For the first line passing through (3, 7) and (-2, -5):
The formula to calculate the slope (m) of a line passing through two points (x1, y1) and (x2, y2) is:
m = (y2 - y1) / (x2 - x1)
Using the given points (3, 7) and (-2, -5), we can calculate the slope of the first line:
m1 = (-5 - 7) / (-2 - 3)
= -12 / -5
= 12/5
Now, let's calculate the slope for the second line passing through (4, 8) and (10, -2):
m2 = (-2 - 8) / (10 - 4)
= -10 / 6
= -5/3
Since the slopes of the two lines, m1 and m2, are different, it means that the lines are not parallel.
Therefore, the answer is: Yes, these lines are not parallel and may intersect.
To determine if the lines intersect or are parallel, we can calculate the slopes of both lines.
The slope of the line passing through (3, 7) and (-2, -5) is given by:
m1 = (y2 - y1) / (x2 - x1)
= (-5 - 7) / (-2 - 3)
= -12 / -5
= 12/5
= 2.4
Similarly, the slope of the line passing through (4, 8) and (10, -2) is:
m2 = (-2 - 8) / (10 - 4)
= -10 / 6
= -5/3
= -1.67
Since the slopes of the two lines are not equal, the lines are not parallel. Therefore, the lines do intersect.