Does the line through (3, 7) and (-2, -5) intersect with the line through (4, 8) and (10, -2)?
Yes…these lines are perpendicular
You cannot tell without a graph
Yes…these lines are not parallel
No…these lines are parallel
Yes…these lines are parallel
No…these lines are perpendicula
You cannot tell without a graph
Yes…these lines are not parallel
In order to determine if the lines intersect or not, we need to first find the slopes of the two 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)
Let's find the slopes of the two lines:
Line 1: Passing through (3, 7) and (-2, -5)
slope1 = (-5 - 7) / (-2 - 3) = -12 / -5 = 12 / 5
Line 2: Passing through (4, 8) and (10, -2)
slope2 = (-2 - 8) / (10 - 4) = -10 / 6 = -5 / 3
Now, if the slopes of the two lines are equal, they are parallel. If the product of the slopes is -1, then the two lines are perpendicular.
Let's check:
slope1 * slope2 = (12 / 5) * (-5 / 3) = -12 / 3 = -4
Since the product of the slopes is not -1, we can conclude that the two lines are parallel.
Therefore, the correct answer is: No, these lines are parallel.