Question

A rectangle has two opposite vertices at the points 1, 2 and 5, 5 if the other vertices lie on the line x = 23 find the equation of sides of rectangle

Answer 1

So, other 2 vertices are B(3,1) and D(3,6).Now, equation of line joining (x1,y1) and (x2,y2) isy−y1x−x1 = y2−y1x2−x1So, equation of AB joining A(1,2) and B(3,1) isy−2x−1 = 1−23−1⇒x+y = 3equation of BC joining B(3,1) and C(5,5) isy−1x−3 = 42⇒2x−y = 5equation of CD joining C(5,5) and D(3,6) is    y−6x−3 = −12⇒x+2y= 15equation of DA joining D(3,6) and A(1,2) is    y−2x−1 = 42⇒2x−y = 2