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

Question

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 B is perpendicular to line C.
Line upper B 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.

Answer 1

To determine which lines are perpendicular, we can analyze the slopes of each line. Two lines are perpendicular if the product of their slopes equals -1 (meaning their slopes are negative reciprocals of each other).

1. Identify the coordinates of the lines: If you can determine the coordinates of any two points on each line, you can find the slope using the formula:

   \[ \text{slope} (m) = \frac{y_2 - y_1}{x_2 - x_1} \]

   where \( (x_1, y_1) \) and \( (x_2, y_2) \) are two points on the line.

2. Calculate the Slopes: After getting the slopes of each line, check for perpendicularity by checking if the product of slopes is -1.

Without the specific coordinates or equations of lines A, B, C, and D, I can't calculate the exact slopes. However, once you find the slopes, simply check which pairs satisfy the condition of being negative reciprocals.

Example: If:

• Line A has a slope of 2.
• Line C has a slope of -1/2.

Then, since \( 2 \times -1/2 = -1 \), lines A and C are perpendicular.

Once you compute the slopes, compare them according to the conditions above and refer to the responses you provided to conclude which lines are perpendicular. If you provide the specific coordinates or the equations of the lines, I can help you compute the slopes directly!