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Find the equations of the diagonal of a rectangle whose sides are x+1=0,x-4=0,y+1=0 and y-2=0.

Asked by Ananya 20th February 2018, 2:56 PM
Answered by Expert
Answer:
begin mathsize 16px style Consider comma
straight x minus 1 equals 0 rightwards double arrow straight x equals 1
similarly space we space get space straight x equals 4 comma space straight y equals negative 1 comma space straight y equals 2
Points space are space straight A left parenthesis 1 comma space minus 1 right parenthesis comma space straight B left parenthesis 1 comma 2 right parenthesis comma space straight C left parenthesis 4 comma negative 1 right parenthesis comma space straight D left parenthesis 4 comma 2 right parenthesis
Diagonal space AD colon
straight A left parenthesis 1 comma space minus 1 right parenthesis space and space straight D left parenthesis 4 comma 2 right parenthesis
fraction numerator straight y minus left parenthesis negative 1 right parenthesis over denominator straight x minus 1 end fraction equals fraction numerator 2 minus left parenthesis negative 1 right parenthesis over denominator 4 minus 1 end fraction
fraction numerator straight y plus 1 over denominator straight x minus 1 end fraction equals 3 over 3
straight y plus 1 equals straight x minus 1
straight x minus straight y minus 2 equals 0
Diagonal space BC colon
straight B left parenthesis 1 comma 2 right parenthesis comma space straight C left parenthesis 4 comma negative 1 right parenthesis
fraction numerator straight y minus 2 over denominator straight x minus 1 end fraction equals fraction numerator negative 1 minus 2 over denominator 4 minus 1 end fraction
fraction numerator straight y minus 2 over denominator straight x minus 1 end fraction equals negative 1
straight y minus 2 equals negative straight x plus 1
straight x plus straight y minus 3 equals 0 end style
Answered by Expert 20th February 2018, 3:14 PM
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