Question

if two opposite vertex of a rectangle are (1,-3) and (4,0) find the co-ordinate of other two vertex​

Answer 1

Answer:

y² - 3y  + x² - 3x + 4 = 0

other vertices will lies on this circle

Step-by-step explanation:

two opposite vertices of an rectangle are - 1, 3 and 4, 0

Let say Vertex of another corner = (x , y)

(x , y) with (-1 , 3)  & ( 4 , 0) will be perpendicular to each other as it is a rectangle

=> ( y - 3)/(x + 1)  * (y - 0)/(x - 4)  = -1

=> y² - 3y   = (x + 1)(4 - x)

=> y² - 3y = -x² + 3x + 4

=> y² - 3y  + x² - 3x + 4 = 0

or

Also   ( 4 - (-1))² + (0 -(3)² = (y - 3)²  + (x - (-1))² + (y - 0)² + (x - 4)²

=>34 = y² + 9 - 6y + x² + 1 + 2x + y² + x² + 16 - 8x

=> 2y² - 6y + 2x² -6x  + 8 = 0

=> y² - 3y  + x² - 3x + 4 = 0

y² - 3y  + x² - 3x + 4 = 0

other vertices will lies on this

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