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A coordinate graph shows both the x and y axes ranging from negative 5 to 5 in unit increments. Four lines are plotted.

Find the slopes of the lines to determine which lines are perpendicular.

(1 point)
Responses

Line A is perpendicular to line C.
Line upper A is perpendicular to line upper C .

Line C is perpendicular to line D.
Line upper C is perpendicular to line upper D .

Line A is perpendicular to line D.
Line upper A is perpendicular to line upper D .

Line B is perpendicular to line C.

1 answer

To determine which lines are perpendicular, we need to find the slopes of the lines plotted on the graph. Two lines are perpendicular if the product of their slopes is -1 (i.e., their slopes are negative reciprocals of each other).

Since I can't see the image or the lines plotted, I'll explain how you can do this:

  1. Find the slope of each line: You can calculate the slope \( m \) of a line using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] where \( (x_1, y_1) \) and \( (x_2, y_2) \) are any two points on the line.

  2. Compare slopes: Once you have the slopes of lines A, B, C, and D:

    • If \( m_A \) is the slope of line A and \( m_C \) is the slope of line C, check if \( m_A \times m_C = -1 \).
    • Repeat this for line pairs (A and D, B and C, and C and D).

  3. Check for perpendicular pairs: Identify which lines have slopes that are negative reciprocals of each other.

If you find the slopes based on this method, you can select the correct answer from the options provided.

If you have access to the equation or points of the lines, please share them, and I can help calculate the slopes.