Does the line through (3, 7) and (-2, -5) intersect with the line through (4, 8) and (10, -2)?(1 point)
Responses
No…these lines are perpendicular
No…these lines are perpendicular
Yes…these lines are perpendicular
Yes…these lines are perpendicular
Yes…these lines are not parallel
Yes…these lines are not parallel
Yes…these lines are parallel
Yes…these lines are parallel
You cannot tell without a graph
You cannot tell without a graph
No…these lines are parallel
You cannot tell without a graph
You cannot tell without a graph.
To determine if two lines intersect, are perpendicular, or parallel, you can use the slope-intercept form of the equation for a line, which is y = mx + b, where m is the slope and b is the y-intercept.
To find the slope of the line through (3, 7) and (-2, -5), you can use the formula (change in y) / (change in x):
m1 = (7 - (-5)) / (3 - (-2)) = 12 / 5
To find the slope of the line through (4, 8) and (10, -2):
m2 = (8 - (-2)) / (4 - 10) = 10 / -6 = -5 / 3
If two lines are perpendicular, their slopes are negative reciprocals of each other. In other words, if m1 * m2 = -1, then the lines are perpendicular.
For these lines, m1 * m2 = (12 / 5) * (-5 / 3) = -4, which is not equal to -1. Thus, the lines are not perpendicular.
If the two lines have the same slope, they are parallel. In this case, m1 is not equal to m2, so the lines are not parallel.
Therefore, the correct answer is: No, these lines are not perpendicular, not parallel, and you can determine this without a graph.