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 parallel
No…these lines are parallel
No…these lines are perpendicular
No…these lines are perpendicular
Yes…these lines are parallel
Yes…these lines are parallel
Yes…these lines are not parallel
Yes…these lines are not parallel
Yes…these lines are perpendicular
Yes…these lines are perpendicular
You cannot tell without a graph
You cannot tell without a graph
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), you can find the slopes of the two lines.
The slope of the line through (3, 7) and (-2, -5) is given by the formula:
m1 = (y2 - y1) / (x2 - x1)
= (-5 - 7) / (-2 - 3)
= (-12) / (-5)
= 12/5
The slope of the line through (4, 8) and (10, -2) is given by the formula:
m2 = (y2 - y1) / (x2 - x1)
= (-2 - 8) / (10 - 4)
= (-10) / 6
= -5/3
Since the slopes of the two lines, 12/5 and -5/3, are not equal, the lines are not parallel.
Therefore, the answer is:
Yes, these lines are not parallel.
To determine if the lines intersect, we can find the slopes of both lines and see if they are equal.
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
Since the slopes of the two lines, 12/5 and -5/3, are not equal, the lines are not parallel. Therefore, the correct response is:
Yes…these lines are not parallel