+847 On the Cartesian plane, the midpoint between two points A(a,b) and B(c,d) is M(m,n) . If A is moved vertically upwards 20 units and horizontally to the right 14 units, and B is moved vertically downwards 4 units and horizontally to the left 2 units, then the new midpoint between A and B is M′. What is the distance between M and M′ ?
+9488 M = midpoint of (a, b) and (c, d) =(a+c2,b+d2)
M' = midpoint of (a+14, b+20) and (c-2, d-4) =((a+14)+(c−2)2,(b+20)+(d−4)2) =(a+c+122,b+d+162) =(a+c2+122,b+d2+162) =(a+c2+6,b+d2+8)
distance between M and M' =√(difference in x values)2+(difference in y values)2 =√62+82 =√100 =10
+9488 M = midpoint of (a, b) and (c, d) =(a+c2,b+d2)
M' = midpoint of (a+14, b+20) and (c-2, d-4) =((a+14)+(c−2)2,(b+20)+(d−4)2) =(a+c+122,b+d+162) =(a+c2+122,b+d2+162) =(a+c2+6,b+d2+8)
distance between M and M' =√(difference in x values)2+(difference in y values)2 =√62+82 =√100 =10
