SOLUTION: The midpoint of the line segment from A to B is (5,-4). If B = (7,-2), what is A?

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Question 1209062: The midpoint of the line segment from A to B is (5,-4). If B = (7,-2), what is A?
Found 4 solutions by mccravyedwin, math_tutor2020, greenestamps, ikleyn:
Answer by mccravyedwin(406)   (Show Source): You can put this solution on YOUR website!

This is really a look-and-see problem if you have graph paper.
Let's call the midpoint M(5,-4).  Notice that M is 2 units left
and 2 units down from B. Since M is the midpoint of AB, you know 
that A has to be two units left and 2 units down from M. The
green line MB is half of AB.



So let's redraw the graph, and you can locate A by observing what point
is 2 units left and 2 units down from M. We'll draw the lower half of AB,
which is AM.  So what are the coordinates of A?  I don't need to tell you,
right?  You can look and see! 




Edwin
Answer by math_tutor2020(3816)   (Show Source): You can put this solution on YOUR website!

A = (x,y)
B = (7,-2)
M = (5,-4) = midpoint of segment AB.

To find the x coordinate of the midpoint, we add the x coordinates of A and B.
Then divide in half.
(x+7)/2 = 5
I'll let the student solve from here.

Similarly, the y coordinate set up equation would be:
(y-2)/2 = -4
I'll let the student solve from here.
Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!


From the midpoint (5,-4) to B(7,-2) is 2 units RIGHT from 5 to 7 and 2 units UP from -4 to -2.

To get from the midpoint to A, we need to move the same distances in the opposite directions from the midpoint.

2 units LEFT from 5 is 3; 2 units DOWN from -4 is -6. A is (3,-6).
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.

Point  " A "  is the mirror reflection of point  B  in the mirror,
if the mirror is established at the midpoint and directed to point  B.

By knowing it,  you do the rest mechanically.



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