Does the line through (3, 7) and (-2, -5) intersect with the line through (4, 8) and (10, -2)?(1 point) Responses You cannot tell without a graph You cannot tell without a graph No…these lines are parallel No…these lines are parallel Yes…these lines are not parallel Yes…these lines are not parallel No…these lines are perpendicular No…these lines are perpendicular Yes…these lines are perpendicular Yes…these lines are perpendicular Yes…these lines are parallel
No…these lines are parallel
To determine if the lines intersect or are parallel, you can calculate their slopes. The formula to find the slope between two points (x1, y1) and (x2, y2) is given by:
slope = (y2 - y1) / (x2 - x1)
For the first line through (3, 7) and (-2, -5):
slope1 = (-5 - 7) / (-2 - 3) = (-12) / (-5) = 12/5
For the second line through (4, 8) and (10, -2):
slope2 = (-2 - 8) / (10 - 4) = (-10) / 6 = -5/3
Since the slopes are different (12/5 and -5/3), the lines are not parallel. Therefore, the lines intersect.
To determine if the lines intersect or are parallel, we can use the slope-intercept form of a line, which is y = mx + b, where m is the slope of the line and b is the y-intercept.
Let's find the slope of the first line using the points (3, 7) and (-2, -5):
m1 = (y2 - y1) / (x2 - x1)
= (-5 - 7) / (-2 - 3)
= (-12) / (-5)
= 12/5
Next, let's find the slope of the second line using the points (4, 8) and (10, -2):
m2 = (y2 - y1) / (x2 - x1)
= (-2 - 8) / (10 - 4)
= (-10) / 6
= -5/3
Since the slopes are not equal, the lines are not parallel.
To determine if the lines are perpendicular or intersecting, we can check if the product of their slopes is -1.
m1 * m2 = (12/5) * (-5/3)
= -1
Since the product of the slopes is -1, the lines are perpendicular and intersect at a point.
Therefore, the correct answer is:
Yes, these lines are perpendicular.