# SOLUTION: Hi. How would I use the distance, midpoint and slope formula to find where a point should go to make a parallelogram? Because on this homework it shows point A(7,12) B(15,4) C(9,2)

Algebra ->  -> SOLUTION: Hi. How would I use the distance, midpoint and slope formula to find where a point should go to make a parallelogram? Because on this homework it shows point A(7,12) B(15,4) C(9,2)      Log On

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 Question 113923: Hi. How would I use the distance, midpoint and slope formula to find where a point should go to make a parallelogram? Because on this homework it shows point A(7,12) B(15,4) C(9,2) D(3,5) The question is to move Point B so that it makes a parallelogram. How would I know where to move it? Thank You for your help!Answer by stanbon(60778)   (Show Source): You can put this solution on YOUR website!How would I use the distance, midpoint and slope formula to find where a point should go to make a parallelogram? Because on this homework it shows point A(7,12) B(15,4) C(9,2) D(3,5) The question is to move Point B so that it makes a parallelogram. How would I know where to move it? Thank You for your help! ---------------------- Plot the points A, C, and D. AB has to be parallel to DC. The slope of DC = (2-5)/(9-3) = -3/6 = -1/2 So the slope of AB as to be -1/2. AB also has to pass thru A(7,12) ------ Line AB has the form y=mx+b where y = 12 when x=7, and m = -1/2 12 = (-1/2)7 + b b = 24/2 +7/2 = 31/2 AB has equation y = (-1/2)x+31/2 --------------------- Line AD has slope (12-5)/(7-3) = 7/4 Line CB must has the same slope and must pass thru C(9,2) 2 = (7/4)9 + b b = 8/4 -63/4 = -55/4 CB has equation y = (7/4)x-55/4 -------------------------------- B is at the intersection of AB and CB. (-1/2)x + (31/2) = (7/4)x-(55/4) (9/4)x = 117/4 x = 13 ----------- Substitute into y = (-1/2)x+31/2 to solve for y: y = (-1/2)(13)+(31/2) y = -13/2 + 31/2 y = 9 ------------ Coordinates of B need to be (13,9) ============== Cheers, Stan H.