In the standard (x,y) coordinate plane, point M with coordinates (5,4) is the midpoint of AB, B has coordinates (7,3). What is the coordinate of A?
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(9,5)
To find the coordinate of point A, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint of two points is the average of their coordinates.
Let's assume the coordinates of point A as (x, y).
According to the midpoint formula,
Midpoint: ((x1+x2)/2, (y1+y2)/2)
where (x1, y1) and (x2, y2) are the coordinates of points A and B, respectively.
Given that point M with coordinates (5,4) is the midpoint of AB, and B has the coordinates (7,3), we can substitute these values into the midpoint formula:
Midpoint: ((x+7)/2, (y+3)/2) = (5, 4)
Now we can set up the equations and solve for x and y:
(x+7)/2 = 5 --> x+7 = 10 --> x = 10 - 7 --> x = 3
(y+3)/2 = 4 --> y+3 = 8 --> y = 8 - 3 --> y = 5
Therefore, the coordinate of point A is (3, 5).