given the points ( g(5,3) ), ( h(-3,2) ), ( i(5,2) ), and ( j(-3,1) ), prove or disprove that ( overline{gh}congoverline{ij} ).
drag and drop the answers to the boxes to complete the solution.
using the distance formula, we solve the lengths of ( gh ) and ( ij ) as follows:
( gh=sqrt{(-3 - 5)^{2}+(2 - 3)^{2}} )
( ij=sqrt{(-3 - 5)^{2}+(1 - 2)^{2}} )
we see that ( overline{gh} ) and ( overline{ij} ) has
therefore, we that ( overline{gh}congoverline{ij} ).

Question

Accepted Answer

# Explanation:
## Step1: Calculate the length of $GH$
Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For points $G(5,3)$ and $H(-3,2)$, $x_1 = 5,y_1=3,x_2=-3,y_2 = 2$.
$$
\begin{align*}
GH&=\sqrt{(-3 - 5)^2+(2 - 3)^2}\
&=\sqrt{(-8)^2+(-1)^2}\
&=\sqrt{64 + 1}\
&=\sqrt{65}
\end{align*}
$$
## Step2: Calculate the length of $IJ$
For points $I(5,2)$ and $J(-3,1)$, $x_1 = 5,y_1=2,x_2=-3,y_2 = 1$.
$$
\begin{align*}
IJ&=\sqrt{(-3 - 5)^2+(1 - 2)^2}\
&=\sqrt{(-8)^2+(-1)^2}\
&=\sqrt{64+1}\
&=\sqrt{65}
\end{align*}
$$

# Answer:
Since $GH=\sqrt{65}$ and $IJ = \sqrt{65}$, we can say that $\overline{GH}\cong\overline{IJ}$ (because segments with equal lengths are congruent).

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the length of \(GH\)

Step2: Calculate the length of \(IJ\)

Answer: