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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

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

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

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

Line C is perpendicular to line D.

3 answers

To determine which lines are perpendicular, we need to find the slopes of each line on the graph. Two lines are perpendicular if the product of their slopes is -1 (meaning one slope is the negative reciprocal of the other).

Without the image, I can't calculate the exact slopes, but you can do it as follows:

  1. Identify the coordinates of two points on each line (at least one point should be easily visible).

  2. Use the formula for slope (m) between two points (x1, y1) and (x2, y2): \[ m = \frac{y2 - y1}{x2 - x1} \]

  3. Calculate the slopes for lines A, B, C, and D.

  4. Once you have the slopes:

    • Check the ratio of slopes of pairs of lines to see if their product is -1.

Based on the options provided, if you find:

  • For example, if the slope of line B is mB and the slope of line C is mC, check if \(mB * mC = -1\).
  • Repeat for each pair based on the options.

Once you've calculated this, you can select the appropriate response based on your findings.

If you have the slopes:

  • If Line B has a slope of \(mB \) and Line C has a slope of \(mC\) such that \( mB \cdot mC = -1 \), then the correct response would be: "Line B is perpendicular to line C."
  • Continue checking other line pairs until you've identified the correct relationships.

Feel free to provide the slopes or a more detailed description if you’d like further help!

whats the answer

I apologize for the earlier confusion, but since I cannot see the image of the coordinate graph, I cannot provide the exact answer without knowing the slopes of the lines.

However, you can determine the correct answer by following the method I provided to calculate the slopes for each line. Here’s a quick recap:

  1. Calculate the slope of each line using two points for each line.
  2. Identify pairs of lines where the product of their slopes equals -1 (indicating they are perpendicular).

Once you perform these calculations, you can choose from the options you've provided:

  • Line B is perpendicular to line C.
  • Line A is perpendicular to line D.
  • Line A is perpendicular to line C.
  • Line C is perpendicular to line D.

Without knowing the slopes or seeing the graph, I cannot definitively tell you which lines are perpendicular. If you share the slopes or more details about the lines, I can help you determine which answer is correct!