Is the point (- 2,-1),(1, 0), (X, 3)and(1, Y)  from a parallelogram find the values of X and Y? Without using the distance formula
 

Asked by hemanttkumarr | 3rd Oct, 2017, 08:27: PM

Expert Answer:

begin mathsize 16px style Slope space of space the space line space joining space open parentheses negative 2 comma space minus 1 close parentheses comma space open parentheses 1 comma space 0 close parentheses space is
fraction numerator 0 minus open parentheses negative 1 close parentheses over denominator 1 minus open parentheses negative 2 close parentheses end fraction equals 1 third
Slope space of space the space line space joining space open parentheses straight X comma space 3 close parentheses space and space open parentheses 1 comma space straight Y close parentheses space is
fraction numerator straight Y space minus space 3 over denominator 1 space minus space straight X end fraction
As space given space points space form space straight a space parallelogram space Slope space of space the space line space joining space open parentheses negative 2 comma space minus 1 close parentheses comma space open parentheses 1 comma space 0 close parentheses space
and space Slope space of space the space line space joining space open parentheses straight X comma space 3 close parentheses space and space open parentheses 1 comma space straight Y close parentheses space are space equal.
fraction numerator straight Y space minus space 3 over denominator 1 space minus space straight X end fraction equals 1 third
3 straight Y space minus space 9 space equals space 1 space minus space straight X
straight X space plus space 3 straight Y space minus space 10 space equals space 0............. left parenthesis straight i right parenthesis
Slope space of space the space line space joining space left parenthesis 1 comma space 0 right parenthesis space and space left parenthesis 1 comma space straight Y right parenthesis space is space 1 over 0.
Slope space of space the space line space joining space open parentheses negative 2 comma space minus 1 close parentheses space and space open parentheses straight X comma space 3 close parentheses
fraction numerator negative 4 over denominator negative 2 space minus space straight X end fraction space equals fraction numerator 1 space over denominator 0 end fraction
fraction numerator negative 2 space minus space straight X over denominator negative 4 end fraction equals 0
space minus 2 space minus space straight X space equals space 0
straight X space equals space minus 2
Put space it space in space the space equation space left parenthesis straight i right parenthesis space we space get
straight Y space equals space 4 end style

Answered by Sneha shidid | 4th Oct, 2017, 10:23: AM