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 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 Yes…these lines are parallel Yes…these lines are parallel You cannot tell without a graph

Question

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 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 Yes…these lines are parallel Yes…these lines are parallel You cannot tell without a graph

Answer 1

You cannot tell without a graph.

Answer 2

To determine if the line through (3, 7) and (-2, -5) intersects with the line through (4, 8) and (10, -2), we can calculate the slopes of both lines.

The slope of the first line can be found using the formula:

m1 = (y2 - y1) / (x2 - x1)

Substituting the coordinates (3, 7) and (-2, -5), we get:

m1 = (-5 - 7) / (-2 - 3)
= -12 / -5
= 12/5

The slope of the second line can be found using the same formula:

m2 = (y4 - y3) / (x4 - x3)

Substituting the coordinates (4, 8) and (10, -2), we get:

m2 = (-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.

Answer 3

To determine if the lines intersect, 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):
slope = (-5 - 7) / (-2 - 3) = -12 / -5 = 12/5

For the second line passing through (4, 8) and (10, -2):
slope = (-2 - 8) / (10 - 4) = -10 / 6 = -5/3

Since the slopes of the two lines are not equal, the lines are not parallel.

To determine if the lines are perpendicular, we can check if the product of their slopes equals -1.

If two lines are perpendicular, their slopes are negative reciprocals of each other.

The product of the slopes 12/5 and -5/3:
(12/5) * (-5/3) = -1

Since the product of the slopes equals -1, the lines are perpendicular.

Therefore, the correct answer is: Yes, these lines are perpendicular.