Question

Does the line through (3, 7) and (-2, -5) intersect with the line through (4, 8) and (10,-2)? (1 point)

A. No...these lines are parallel

B. Yes...these lines are perpendicular

C. No...these lines are perpendicular

D. You cannot tell without a graph

E. Yes...these lines are parallel

F. Yes...these lines are not parallel

Answer 1

Are you sure

Answer 2

To determine if the lines intersect, we need to find the slopes of both lines.

The slope of the line passing through (3, 7) and (-2, -5) can be calculated using the slope formula:
m = (y2 - y1) / (x2 - x1)
= (-5 - 7) / (-2 - 3)
= (-12) / (-5)
= 12/5

The slope of the line passing through (4, 8) and (10, -2) can also be calculated:
m = (-2 - 8) / (10 - 4)
= (-10) / 6
= -5/3

If the slopes of the two lines are equal, they are parallel and do not intersect.

If the slopes are negative reciprocals of each other, the lines are perpendicular and do intersect.

Comparing the slopes, 12/5 and -5/3 are neither equal nor negative reciprocals of each other. Therefore, the lines are not parallel or perpendicular.

So, the correct answer is F. Yes...these lines do not parallel.

Answer 3

I apologize, I made a mistake in my previous response.

Upon recalculating the slopes, the slope of the line passing through (3, 7) and (-2, -5) is:

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

The slope of the line passing through (4, 8) and (10, -2) is:

m = (-2 - 8) / (10 - 4) = -10 / 6 = -5/3

Since the slopes are not equal and not negative reciprocals of each other, the lines are neither parallel nor perpendicular. Thus, the lines do intersect.

The correct answer is F. Yes, these lines do intersect.