To find a point that lies on a line parallel to another line and passing through a specific point, we first need to determine the slope of the original line.
The points given are (12, 8), (6, 6), (2, 8), and (6, 0). We can calculate the slope using any two of these points. Let’s use the points (12, 8) and (6, 6).
The formula for the slope (m) between two points (x1, y1) and (x2, y2) is:
m = (y2 - y1) / (x2 - x1)
Using (12, 8) and (6, 6):
m = (6 - 8) / (6 - 12) = -2 / -6 = 1/3
Now that we know the slope (m = 1/3), we can write the equation of the line that passes through the point (0, 6) using the point-slope formula:
y - y1 = m(x - x1)
Plugging in the point (0, 6):
y - 6 = (1/3)(x - 0) => y - 6 = (1/3)x => y = (1/3)x + 6
This is the equation of the line that is parallel to the original line and passes through (0, 6).
To find a specific point on this line, we can choose any value for x. For example, let’s set x = 3:
y = (1/3)(3) + 6 = 1 + 6 = 7
So, when x = 3, we find that y = 7, which gives us the point (3, 7).
Therefore, a point that lies on the line passing through (0, 6) and parallel to the given line is (3, 7).