Answer:
J (6,2) K (2,2)
Step-by-step explanation:
Now distance of AB = [(y2-y1)^2 + (x2-x1)^2]^(1/2)
= 8 units
CB = [(y2-y1)^2 + (x2-x1)^2]^(1/2)
= 6 units by using same formula
Now AB/CB must equal to GH/HJ as rectangles are similar
GH = [(y2-y1)^2 + (x2-x1)^2]^(1/2)
= 4 units
so
8/6 = 4/HJ
So,
HJ = 3 units
Now if we see the coordinates given carefully, it is obvious that two perpendicular lines lie perfectly parallel to x and y coordinates in rectangle ABCD. A is (-7,-2) and B is (1,-2) which means distance along y-axis doesn't change. Similarly for C (1,-8) and D (-7,-8), one can see that distance between y-axis doesn't change. So lines AB and CD of rectangle are parallel with x and AD and BC are parallel with y-axis.
In rectangle GHJK one can see that in given coordinates, G(2,5) and H(6,5), y coordinate is same so it is parallel to x axis. Now, HJ is perpendicular to GH so it must be parallel to y axis. It means if we know the lengths of sides we can easily determine unknown coordinates by simple addition and subtraction.
So, we know HJ = 3 units
J is (6,2) since HJ is parallel to y axis so distance on x axis will remain unchanged and length of line HJ will effect distance of y axis.
Similarly K is (2,2) for the same reason.
and 
. Get everything on one side of the equals sign, set it equal to 0 and factor. When you do this you get (x-3)(x+27). The Zero Product Property rule tells us that either x-3 = 0 or x+27 = 0 and that x = 3 and -27. The only thing in math that will NEVER be negative besides time is distance/length, therefore, x cannot be 27 and has to be 3.
