Write a two column proof. If ZY=3XY, then ZX=4XY
1 answer:
Answer:
As you have written
Z Y = 3 X Y,
It means X, Y, Z are collinear points i.e they lie in the same line or line segment.
Locating points X, Y,Z on the line
Two possibilities are possible
1. First Z, then X and then Y on the line or line segment
→ Z X + Y X= Z Y
But Z Y = 3 X Y [ Given]
→ Z X + Y X = 3 X Y
→ Z X = 3 X Y - Y X
→ Z X = 2 X Y ⇒ which is not the result.
2. 2nd Possibility
First Z, then Y and then X on the line or line segment
→ Z X = Z Y + Y X
→ Z X= 3 X Y + Y X [Z Y=3 X Y→(given)]
→ Z X= 4 X Y , Which is the result.
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. 
The other terms can't be combined.
Your final answer should be
.
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Your final answer should be