Final answer:
The line passing through the points (3,3) and (7,11) does not intersect the line passing through the points (5,8) and (13,24).
Step-by-step explanation:
To determine if line AB (passing through points A(3,3) and B(7,11)) intersects with line CD (passing through points C(5,8) and D(13,24)), we need to find the equations of both lines and check if they intersect.
The equation of line AB can be found using the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. The slope (m) can be calculated as (y2 - y1) / (x2 - x1), which gives us (11 - 3) / (7 - 3) = 8 / 4 = 2. The y-intercept (b) can be found by substituting one of the points (such as A) into the equation: 3 = 2(3) + b, which gives us b = -3. Therefore, the equation of line AB is y = 2x - 3.
Similarly, the equation of line CD can be found using the same method. The slope (m) is (24 - 8) / (13 - 5) = 16 / 8 = 2, and the y-intercept (b) is found by substituting one of the points (such as C): 8 = 2(5) + b, which gives us b = -2. Therefore, the equation of line CD is y = 2x - 2.
To check if the lines intersect, we can set the two equations equal to each other and solve for x: 2x - 3 = 2x - 2. Since the x terms cancel each other out, we are left with -3 = -2, which is not true. Therefore, the lines do not intersect.