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Parallel and Perpendicular Lines Quick Check

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Question
Use the image to answer the question.

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 which answer is correct and why

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.
Line upper B is perpendicular to line upper C .
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1 answer

To determine which lines are perpendicular based on their slopes, we need to remember that two lines are perpendicular if the product of their slopes is -1.

  1. Calculate the slopes of the lines. If you can provide the coordinates of two points for each line (A, B, C, and D), I can help you find the slopes. The slope \( m \) of a line through two points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated using the formula:

    \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

  2. Evaluate the relationships: Once the slopes are found, multiply the slopes of each pair of lines and check if the result is -1.

Without the specific coordinates for lines A, B, C, and D provided in the image, I can’t calculate the slopes directly. If you provide the coordinates or slopes of the lines, I will then be able to assist you in identifying which lines are perpendicular based on those calculations.