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

Question

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 parallel
Yes…these lines are parallel

Yes…these lines are not parallel
Yes…these lines are not parallel

You cannot tell without a graph
You cannot tell without a graph

No…these lines are parallel

Answer 1

To determine if the two lines intersect, we can calculate their slopes and check their relationship.

1. Line through (3, 7) and (-2, -5):

   • The slope \( m_1 \) is calculated using the formula: \[ m_1 = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-5 - 7}{-2 - 3} = \frac{-12}{-5} = \frac{12}{5} \]

2. Line through (4, 8) and (10, -2):

   • The slope \( m_2 \) is calculated similarly: \[ m_2 = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-2 - 8}{10 - 4} = \frac{-10}{6} = -\frac{5}{3} \]

3. Comparison of slopes:

   • The slopes \( m_1 = \frac{12}{5} \) and \( m_2 = -\frac{5}{3} \) are neither equal nor negative reciprocals of each other (which would mean they are perpendicular).

Since the slopes are different, the lines are not parallel.

Thus, the correct response is: Yes…these lines are not parallel.