Does the line through (3, 7) and (-2, -5) intersect with the line through (4, 8) and (10, -2)?
No…these lines are parallel
No…these lines are parallel
No…these lines are perpendicular
No…these lines are perpendicular
You cannot tell without a graph
You cannot tell without a graph
Yes…these lines are not parallel
Yes…these lines are not parallel
Yes…these lines are parallel
Yes…these lines are parallel
Yes…these lines are perpendicular
No…these lines are perpendicular
You cannot tell without a graph.
To determine if the line through (3, 7) and (-2, -5) intersects with the line through (4, 8) and (10, -2), we need to find the slopes of both lines. 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)
For the first line passing through (3, 7) and (-2, -5), the slope is:
slope1 = (-5 - 7) / (-2 - 3) = (-12) / (-5) = 12/5
For the second line passing through (4, 8) and (10, -2), the slope is:
slope2 = (-2 - 8) / (10 - 4) = (-10) / 6 = -5/3
If the slopes of two lines are equal, then the lines are parallel. If the slopes are negative reciprocals of each other, then the lines are perpendicular.
In this case, the slopes of the two lines, 12/5 and -5/3, are neither equal nor negative reciprocals of each other. Therefore, the lines are neither parallel nor perpendicular.