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Question 1197663: Hi, can you help me answer this?
Three vertices of a parallelogram are ( 5, 12 ), ( 2,7 ) and ( 6, 1 ) joined in the order
named. Find the 4th vertex.
Found 2 solutions by ewatrrr, math_tutor2020:
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website!
Hi
Three vertices of a parallelogram are ( 5, 12 ), ( 2,7 ) and ( 6, 1 ) joined in the order:
Graphing
y = (5/3)x - 9 (green) & y= (-3/2)x + 39/2 (Blue)
4th vertex is P(9,6)
Wish You the Best in your Studies.
Answer by math_tutor2020(3817)  (Show Source):
You can put this solution on YOUR website!
Similar question
https://www.algebra.com/algebra/homework/Length-and-distance/Length-and-distance.faq.question.1197883.html
Let
A = ( 5, 12 )
B = ( 2,7 )
C = ( 6, 1 )
Those vertices form a parallelogram where we connect them in the order shown.
The goal is to find the location of point D to form parallelogram ABCD.
To go from A to B we do two things:
Move left 3 units
Move down 5 units
Think of it like a slope diagram.
To go from B to C, we do these two things
Move right 4 units
Move down 6 units
To go from C to D, we will apply the inverse operations that we used going from A to B.
Instead of going "3 units left", we go "3 units right".
Instead of "move down 5 units" we "go up 5 units".
In short, we'll apply these two steps when going from C to D
Move 3 units right
Move 5 units up
This will guarantee we have CD parallel to AB
Start at C(6,1)
Move 3 units right to arrive at (9,1)
Then move 5 units up to arrive at (9,6) which is the location of point D.
Use the slope formula to find the slopes of AB and CD.
They should be the same value. Parallel lines have equal slopes.
Similarly, slopes BC and AD should be the same value as well.
I'll let the student do these confirmations.
The slope formula is
As a further thing to point out:
If we started at B(2,7) and applied the "move 3 units right, 5 units up" motion pattern, then we would arrive at point A(5,12).
I recommend drawing out the diagram if you are a visual learner. Refer to the diagram the tutor @ewatrrr has provided.
Answer: (9,6)
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