Let A=(0,1), B=(2,5), C=(5,2) and D=(7,0). A figure is created by connecting A to B to C to D The perimeter of ABCD can be expressed in the form (A sqrt2)+(B sqrt5) with A and B integers. What is the sum of A and B?
+23246 Using the distance formula: D = sqrt[ (x2 - x1)2 + (y2 - y1)2 ]
A to B: sqrt[ (2 - 0)2 + (5 - 1)2 ] = sqrt[ (2)2 + (4)2 ] = sqrt( 20 ) = 2sqrt(5)
B to C: sqrt[ (5 - 2)2 + (2 - 5)2 ] = sqrt[ (3)2+ (-3)2 ] = sqrt( 18 ) = 3sqrt(2)
C to D: sqrt[ (7 - 5)2 + (0 - 2)2 ] = sqrt[ (2)2 + (-2)2 ] = sqrt( 8 ) = 2sqrt(2)
D to A: sqrt[ (0 - 7)2 + (1 - 0)2 ] = sqrt[ (-7)2 + (1)2 ] = sqrt( 50 ) = 5sqrt(2)
Can you add these distances together?
+23246 Using the distance formula: D = sqrt[ (x2 - x1)2 + (y2 - y1)2 ]
A to B: sqrt[ (2 - 0)2 + (5 - 1)2 ] = sqrt[ (2)2 + (4)2 ] = sqrt( 20 ) = 2sqrt(5)
B to C: sqrt[ (5 - 2)2 + (2 - 5)2 ] = sqrt[ (3)2+ (-3)2 ] = sqrt( 18 ) = 3sqrt(2)
C to D: sqrt[ (7 - 5)2 + (0 - 2)2 ] = sqrt[ (2)2 + (-2)2 ] = sqrt( 8 ) = 2sqrt(2)
D to A: sqrt[ (0 - 7)2 + (1 - 0)2 ] = sqrt[ (-7)2 + (1)2 ] = sqrt( 50 ) = 5sqrt(2)
Can you add these distances together?
