The coordinates of a point p(a,2a) of line of point m(2a,3) and n(4,3). Find the value of a
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The slope of line MN is 0.
So, every point has y-coordinate 3.
Thus, 2a=3 and P = (3/2,3)
To find the value of "a" for the point P(a, 2a) on the line passing through points M(2a, 3) and N(4, 3), we can use the fact that two points determine a unique line.
We know that the slope of a line passing through two points (x1, y1) and (x2, y2) can be calculated using the formula:
slope(m) = (y2 - y1) / (x2 - x1)
In this case, the coordinates of M are (2a, 3), and the coordinates of N are (4, 3). Therefore, the slope of line MN is:
slope(MN) = (3 - 3) / (4 - 2a)
= 0 / (4 - 2a)
= 0
Since the slope of line MN is 0, it means that the line is parallel to the x-axis. For any point on this line, the y-coordinate remains constant. Therefore, we can determine the value of "a" by comparing the y-coordinate of the given point P(a, 2a) and the y-coordinate of M.
As P(a, 2a) lies on the line MN, its y-coordinate should be 3 as well:
2a = 3
Dividing both sides of the equation by 2, we get:
a = 3/2
Hence, the value of "a" is 3/2.