Question

Write a two column proof. If ZY=3XY, then ZX=4XY

Answer 1

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.