Question 256002: In the standard (x,y) coordinate plane, point M with coordinates (5,4) is the midpoint of AB, and B has coordinates (7,3). What are the coordinates of A ?
A. (17,11) B. ( 9, 2) C. ( 6, 3.5) D. ( 3, 5) E. (−3,−5)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! I would say (3,5) are the coordinates.
line is ABC.
point B is (5,4)
point C is (7,3)
x coordinate of C minus x coordinate of B = 7-5 = 2
y coordinate of C minus y coordinate of B = 3-4 = -1
subtract 2 from x coordinate of B to get x coordinate of A = 3
subtract -1 from y coordinate of B to get y coordinate of A = 5
distance from B to C is equal to square root of ((7-5)^2 + (3-4)^2) = square root of (2^2 + (-1)^2) = square root of (4 + 1) = square root of 5.
distance from A to B is equal to square root of ((5-3)^2 + (4-5)^2 = square root of (2^2 + (-1)^2) = square root of (4 + 1) = square root of 5.
slope intercept form of the equation for these lines would be y = mx + b where m is the slope and b is the y-intercept:
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slope intercept form of the equation for line AB formed by points (x1,y1) = (3,5) and (x2,y2) = (5,4) is created as follows:
slope is (y2-y1) / (x2-x1) = -1/2 = -(1/2)
y-intercept is y1 = -(1/2)*x1 + b becomes 5 = (-1/2)*3 + b becomes 5 = -(3/2) + b becomes b = 5 + (3/2) becomes b = (10/2) + (3/2) becomes b = (13/2)
equation is y = -(1/2)x + (13/2)
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slope intercept form of the equation for line BC formed by points (x1,y1) = (5,4) and (x2,y2) = (7,3) is created as follows:
slope is (y2-y1) / (x2-x1) = -1/2 = -(1/2).
y-intercept is y1 = -(1/2)*x1 + b becomes 4 = -(1/2)*5 + b becomes 4 = -(5/2) + b becomes b = 4 + (5/2) becomes b = (8/2) + (5/2) becomes b = (13/2).
equation is y = -(1/2)x + (13/2).
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since the graphs of line AB and BC are identical, these are the same line.
graph of the equation for this line is shown below:
you can see that when x = 3, y = 5, and when x = 5, y = 4, and when x = 7, y = 3
your answer is selection D (3,5).
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