Question

May I please get help with this. I have tried multiple times but still could not get the correct or at least accurate answers I would appreciate it so much if I could get help with this

Answer 1

The vertices of the given quadrilateral GHJK are:

G = (3, 2)

H = (-3, 3)

J = (-5, -2)

K = (1, -3)

a) To find the length of JK and GH we will use the rule of the distance

`d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}`

For JK, let J = (x1, y1) and K = (x2, y2)

`\begin{gathered} JK=\sqrt[]{(1--5)^2+(-3--2)^2} \\ JK=\sqrt[]{(1+5)^2+(-3+2)^2} \\ JK=\sqrt[]{(6)^2+(-1)^2} \\ JK=\sqrt[]{36+1} \\ JK=\sqrt[]{37} \end{gathered}`

For GH, let G = (x1, y1) and H = (x2, y2)

`\begin{gathered} GH=\sqrt[]{(-3-3)^2+(3-2)^2} \\ GH=\sqrt[]{(-6)^2+(1)^2} \\ GH=\sqrt[]{36+1} \\ GH=\sqrt[]{37} \end{gathered}`

b) We will use the rule of the slope to find the slopes of JK and GH

`m=(y_2-y_1)/(x_2-x_1)`

For JK

`\begin{gathered} m_(JK)=(1--5)/(-3--2) \\ m_(JK)=(1+5)/(-3+2) \\ m_(JK)=(6)/(-1) \\ m_(JK)=-6 \end{gathered}`

For GH

`\begin{gathered} m_(GH)=(-3-3)/(3-2) \\ m_(GH)=(-6)/(1) \\ m_(GH)=-6 \end{gathered}`

c) From parts a and b

JK = GH

JK // GH because they have the same slopes

Then GHJK is a parallelogram because it has a pair of opposite sides that are both congruent and parallel

The answer is A