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

Question

Responses

Yes…these lines are perpendicular
Yes…these lines are perpendicular

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
You cannot tell without a graph

No…these lines are parallel
No…these lines are parallel

Yes…these lines are not parallel

Answer 1

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

1. First Line through points (3, 7) and (-2, -5): The slope (m) is calculated as: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-5 - 7}{-2 - 3} = \frac{-12}{-5} = \frac{12}{5} \]

2. Second Line through points (4, 8) and (10, -2): The slope (m) is calculated as: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-2 - 8}{10 - 4} = \frac{-10}{6} = -\frac{5}{3} \]

Now we have the slopes of both lines:

• Slope of the first line = \(\frac{12}{5}\)
• Slope of the second line = \(-\frac{5}{3}\)

Now, let's check if they are parallel:

• Lines are parallel if their slopes are equal.
• \(\frac{12}{5} \neq -\frac{5}{3}\), so the lines are not parallel.

Next, let's check if they are perpendicular:

• Lines are perpendicular if the product of their slopes is -1: \[ \frac{12}{5} \cdot -\frac{5}{3} = \frac{-60}{15} = -4 \quad (\text{not } -1) \] Thus, they are not perpendicular.

Since the lines are not parallel and not perpendicular, they must intersect.

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