AB¯¯¯¯¯¯¯¯ has endpoints A and B, with point A at (6,5). AB¯¯¯¯¯¯¯¯ has midpoint M at (4,6). What are the coordinates of point B?

Question

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Answer 1

Answer: B = (2,7)

Simplest way is look how you got to M from A: x decreased by 2 (from 6 to 4) and y increased 1 (from 5 to 6). So do that a 2nd time to get to B: decrease 4 by 2 to get x=2 and increase 6 to 7 y=7. the point B is (2,7)

Distance from A to M is square root of (6-4)^2 + (5-6)^2 = sqr(4+1) = square root of 5

Also get the equation for the line AB: rise/run = (y-6)/(x-4) = (5-6)/6-4)=-1/2 = slope = difference in y values divided by the difference in x values of the two points

y-6 = (-1/2)(x-4)

or y= (-1/2)(x-4) + 6

y=(-1/2)(x) +2 + 6 = --x/2 +8

8 is the y intercept, -1/2 = slope of the line. It's going downhill on a graph

You went downhill a distance of square root of 5 to get to the midpoint. Now you go an equal distance further downhill to get point B

Point B is (x,y) such that the distance from (x,y) to the midpoint equals square root of 5

From (2,7) to (4,6) is a distance of sqr5 = sqr(1+4)