Does the line through (3, 7) and (-2, -5) intersect with the line through (4, 8) and (10, -2)?(1 point)
Responses
Yes…these lines are perpendicular
Yes…these lines are perpendicular
Yes…these lines are not parallel
Yes…these lines are not parallel
No…these lines are perpendicular
No…these lines are perpendicular
No…these lines are parallel
No…these lines are parallel
You cannot tell without a graph
You cannot tell without a graph
Yes…these lines are parallel
No...these lines are parallel
No, these lines are parallel.
To determine whether the lines through (3, 7) and (-2, -5) and through (4, 8) and (10, -2) intersect, we can find the slopes of both lines. If the slopes are equal, the lines are parallel and do not intersect. If the slopes are different, the lines are not parallel and intersect at some point.
The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula:
slope = (y2 - y1) / (x2 - x1)
Let's calculate the slope of each line:
Slope of the line through (3, 7) and (-2, -5):
slope = (-5 - 7) / (-2 - 3) = -12 / -5 = 12/5
Slope of the line through (4, 8) and (10, -2):
slope = (-2 - 8) / (10 - 4) = -10 / 6 = -5/3
Since the slopes are not equal, the lines are not parallel and will intersect at some point.