Does the line through (3, 7) and (-2, -5) intersect with the line through (4, 8) and (10, -2)?(1 point)
Responses
To determine if the two lines intersect, we can calculate the slopes of both lines.
The slope of the first line passing through (3, 7) and (-2, -5) is:
m1 = (y2 - y1)/(x2 - x1)
= (-5 - 7)/(-2 - 3)
= -12/-5
= 12/5
The slope of the second line passing through (4, 8) and (10, -2) is:
m2 = (y2 - y1)/(x2 - x1)
= (-2 - 8)/(10 - 4)
= -10/6
= -5/3
If the slopes of the two lines are equal, then they are parallel and do not intersect. If the slopes are different, then the lines will intersect.
In this case, the slopes are different (12/5 and -5/3), so the two lines intersect.
To determine if the two lines intersect, we can find the slopes of the lines and see if they are equal.
The slope of the first line passing through (3, 7) and (-2, -5) is given by:
m1 = (y2 - y1) / (x2 - x1)
= (-5 - 7) / (-2 - 3)
= (-12) / (-5)
= 12/5
The slope of the second line passing through (4, 8) and (10, -2) is given by:
m2 = (y2 - y1) / (x2 - x1)
= (-2 - 8) / (10 - 4)
= (-10) / 6
= -5/3
Since the slopes of the two lines are not equal (m1 ≠ m2), the lines will intersect at some point.
To determine if the line through (3, 7) and (-2, -5) intersects with the line through (4, 8) and (10, -2), we can use the concept of slope.
First, let's find the slope of the first line. The formula to calculate the slope (m) between two points (x1, y1) and (x2, y2) is:
m = (y2 - y1) / (x2 - x1)
Using the given points (3, 7) and (-2, -5), we can substitute the values into the formula:
m1 = (-5 - 7) / (-2 - 3)
Simplifying this expression gives us:
m1 = (-12) / (-5)
m1 = 12/5 or 2.4
Now, let's find the slope of the second line. Using the points (4, 8) and (10, -2):
m2 = (-2 - 8) / (10 - 4)
m2 = (-10) / 6
m2 = -5/3 or -1.67
If two lines in a coordinate plane don't intersect, their slopes will be equal. So, let's compare the slopes we found.
m1 = 2.4 and m2 = -1.67
Since 2.4 ≠ -1.67, we can conclude that the lines do intersect.