Rectangle ABCD has vertices at (-7,-2); (1, -2); (1, -8); and (-7, -8) respectively. If GHJK is a similar rectangle where G(2, 5) and H(6, 5); where could points J and K be located? Group of answer choices
Points J and K could be located at:
J(2,2)
K(6,2)
Step-by-step explanation:
Consider the vertices have a x and y coordinate:
A: x coordinate=-7 y coordinate=-2
B: x coordinate=1 y coordinate=-2
C: x coordinate=1 y coordinate=-8
D: x coordinate=-7 y coordinate=-8
G: x coordinate=2 y coordinate=5
H: x coordinate=6 y coordinate=5
Then it is possible to calculate the distance between the x and y coordinates:
x coordinate of Vertices AB:
x coordinate of B- x coordinate of A=1-(-7)=8
The distance between A and B is 8
y coordinate of Vertices AC:
y coordinate of A- y coordinate of C=-2-(-8)=6
The distance between A and C is 6
Then we know that the side AB of Rectangle ABCD measures 8 and the side AC, measures 6.
Repeat the analysis with Rectangle GHJK. In this case, is only possible to calculate the distance with x coordinate.
x coordinate of Vertices GH:
x coordinate of H- x coordinate of G=6-(2)=4
The distance between G and H is 4
We can see that the distance in x of the Rectangle ABCD is 8, and the distance in x of the Rectangle GHJK is 4, it means that the measure of ABCD is twice GHJK.
Then, if the distance in y coordinate of Vertices AC is 6, we could say that the distance in y coordinate of Vertices GJ is 3.
Points J and K could be located at:
J(2,2)
K(6,2)
the answer is b
hope it you
step-by-step explanation:
sin(7pi/6 - pi/3)
= sin(7pi/6 - 2pi/6)
= sin(5pi/6)
= sin(pi - pi/6)
= sin(pi/6)
= 1/2
sin 7pi/6 - sin pi/3
= sin (pi + pi/6) - sin pi/3
= -sin pi/6 - sin pi/3
= -1/2 - sqrt(3)/2
= -(1+sqrt(3))2