Final answer:
To find the equation of the line AB, we need to find the coordinates of A and B using the given equations. Then, we can find the slope and use it to write the equation of the line AB. The distance between A and B can be found using the distance formula.
Step-by-step explanation:
To find the equation of the line AB, we first need to find the coordinates of points A and B. Since A(x1, y1) lies on the line 3x - 4y = 26, we can substitute x1 and y1 into the equation to find the coordinates. Using the equation, we get 3x1 - 4y1 = 26.
Similarly, since B(y1, x1) lies on the line 5x - 3y + 31 = 0, we can substitute y1 and x1 into the equation. Using the equation, we get 5x1 - 3y1 + 31 = 0.
Once we have the coordinates of points A and B, we can use the slope formula to find the slope of the line AB, which is equal to (y2 - y1) / (x2 - x1). With the slope, we can use the point-slope form of a linear equation to write the equation of the line AB. Finally, to find the distance between A and B, we can use the distance formula.