This MATLAB code calculates and displays the point of intersection...

August 28, 2025 at 07:08 PM

% M2 C: Line intersection point % define constant parameters for two lines m1 = -5 + 10*rand; b1 = -5 + 10*rand; m2 = -5 + 10*rand; b2 = -5 + 10*rand; %To test specific values, UNCOMMENT and DEFINE the variables below and 'Run Script' % Be certain you DELETE or COMMENT OUT these lines before clicking 'Submit' m1 = 1; b1 = 0; m2 = 0; b2 = 3; % display input variables - numerical values are set to 2 decimal places fprintf('m for Line 1: %.2f\nb for Line 1: %.2f\nm for Line 2: %.2f\nb for Line 2: %.2f\n', m1, b1, m2, b2) % solve for x value given two lines x = ((b2-b1)/(m1-b2)) % substitute solution for x into equation for first line y =(m1*x)+b1 % display point of intersection

This MATLAB code calculates and displays the point of intersection of two lines defined by their slopes (m_1, m_2) and y-intercepts (b_1, b_2). Here's what each section does:

  1. Random Initialization of Line Parameters:

    • Slopes ((m_1) and (m_2)) and y-intercepts ((b_1) and (b_2)) for the two lines are initialized using the rand function to generate random numbers between -5 and 5.

  2. Static Testing of Specific Line Values:

    • There is a commented-out block with specific values for (m_1), (b_1), (m_2), and (b_2). If uncommented, these values are used instead of the randomized ones, allowing the user to test specific cases (e.g., (m_1 = 1, b_1 = 0, m_2 = 0, b_2 = 3)).

  3. Display Line Parameters:

    • The fprintf function prints the values of (m_1), (b_1), (m_2), and (b_2) to two decimal places.

  4. Solve for Intersection:

    • The code computes the (x)-coordinate of the intersection of the two lines using the formula: [ x = \frac{b_2 - b_1}{m_1 - m_2} ] This is derived from equating the equations of the two lines: [ y = m_1x + b_1 \quad \text{and} \quad y = m_2x + b_2 ]

  5. Substitute (x) to Compute (y):

    • The computed (x)-value is substituted into the equation of the first line ((y = m_1x + b_1)) to find the (y)-coordinate of the intersection.

  6. (Bug Note):

    • There is a mistake in this code: the calculation of x uses (m1-b2) in the denominator instead of (m1-m2). This will lead to incorrect results unless fixed.

  7. Point of Intersection Display:

    • The output shows the (x)- and (y)-coordinates of the intersection point.

In summary, this code duplicates the interaction for two lines, computes their intersection point, and displays its coordinates, but contains an error in the x calculation that should be fixed to work correctly.

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