Sir,
If the opposite vertices of a square are (-2,3) and (8,5) . find the equations of the square.

Asked by raoss1967 | 27th May, 2015, 10:20: AM

Expert Answer:

Slope of line AC in the above figure is
fraction numerator 5 minus 3 over denominator 8 minus left parenthesis negative 2 right parenthesis end fraction equals 2 over 10 equals 1 fifth
Both the lines AD and AB pass through (-2,3), such that they make an angle of 45o with AC.
Let slope of any one of them be 'm'.
open vertical bar fraction numerator m minus begin display style 1 fifth end style over denominator 1 plus m cross times begin display style 1 fifth end style end fraction close vertical bar equals tan 45 to the power of o rightwards double arrow open vertical bar fraction numerator 5 m minus 1 over denominator 5 plus m end fraction close vertical bar equals 1 rightwards double arrow 5 m minus 1 equals plus-or-minus open parentheses 5 plus m close parentheses rightwards double arrow 5 m minus 1 equals 5 plus m space o r space 5 m minus 1 equals negative open parentheses 5 plus m close parentheses rightwards double arrow m equals 3 over 2 space o r space m equals negative 2 over 3
If we take slope of AD as 3/2, then equation of AD is y-3=3/2 (x+2)
So, slope of AB will be -2/3. Hence, equation of AB is y-3=-2/3 (x+2)
Since, BC is parallel to AD, equation of BC is y-5=3/2 (x-8).
CD is parallel to AB. So, its equation is y-5=-2/3 (x-8).

Answered by satyajit samal | 28th May, 2015, 04:25: PM

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